Publications in international journals
Martin Vohralík
1. Buffa, A., Chanon, O., Grappein, D., Vázquez, R., and Vohralík, M. An
equilibrated flux a posteriori error estimator for defeaturing problems. SIAM
J. Numer. Anal. 62, 6 (2024), 2439–2458. Journal version, paper .
2. Chaumont-Frelet, T., and Vohralík, M. Constrained and unconstrained
stable discrete minimizations for p-robust local reconstructions in vertex
patches in the de Rham complex. Found. Comput. Math. (2024). Journal
version, preprint .
3. Chaumont-Frelet, T., and Vohralík, M. A stable local commuting
projector and optimal hp approximation estimates in H(curl). Numer. Math.
156, 6 (2024), 2293–2342. Journal version, preprint .
4. Févotte, F., Rappaport, A., and Vohralík, M.
Adaptive regularization for the Richards equation. Comput. Geosci. (2024).
DOI 10.1007/s10596-024-10309-7. Journal version, preprint .
5. Mitra, K., and Vohralík, M. A posteriori error estimates for the
Richards equation. Math. Comp. 93, 347 (2024), 1053–1096. Journal version,
preprint .
6. Gantner, G., and Vohralík, M. Inexpensive polynomial-degree-robust
equilibrated flux a posteriori estimates for isogeometric analysis. Math.
Models Methods Appl. Sci. 34, 3 (2024), 477–522. Journal version, preprint .
7. Févotte, F., Rappaport, A., and Vohralík, M. Adaptive regularization,
discretization, and linearization for nonsmooth problems based on
primal-dual gap estimators. Comput. Methods Appl. Mech. Engrg. 418, B
(2024), 116558. Journal version, preprint .
8. Chaumont-Frelet, T., and Vohralík, M. p-robust equilibrated flux
reconstruction in H(curl) based on local minimizations. Application to a
posteriori analysis of the curl–curl problem. SIAM J. Numer. Anal. 61, 4
(2023), 1783–1818. Journal version, paper .
9. Jayadharan, M., Kern, M., Vohralík, M., and Yotov, I. A space-time
multiscale mortar mixed finite element method for parabolic equations. SIAM
J. Numer. Anal. 61, 2 (2023), 675–706. Journal version, paper .
10. Daniel, P., and Vohralík, M. Guaranteed contraction of adaptive inexact
hp-refinement strategies with realistic stopping criteria. ESAIM Math. Model.
Numer. Anal. 57, 1 (2023), 329–366. Journal version, preprint .
11. Ben Gharbia, I., Ferzly, J., Vohralík, M., and Yousef, S. Adaptive
inexact smoothing Newton method for a nonconforming discretization of a
variational inequality. Comput. Math. Appl. 133 (2023), 12–29. Journal
version, preprint .
12. Ben Gharbia, I., Ferzly, J., Vohralík, M., and Yousef, S. Semismooth
and smoothing Newton methods for nonlinear systems with complementarity
constraints: Adaptivity and inexact resolution. J. Comput. Appl. Math. 420
(2023), 114765. Journal version, preprint .
13. Ern, A., Gudi, T., Smears, I., and Vohralík, M. Equivalence of local-
and global-best approximations, a simple stable local commuting projector,
and optimal hp approximation estimates in H(div). IMA J. Numer. Anal.
42, 2 (2022), 1023–1049. Journal version, preprint .
14. Papež, J., and Vohralík, M. Inexpensive guaranteed and efficient upper
bounds on the algebraic error in finite element discretizations. Numer.
Algorithms 89 (2022), 371–407. Journal version, preprint .
15. Chaumont-Frelet, T., Ern, A., and Vohralík, M. Stable broken H(curl)
polynomial extensions and p-robust a posteriori error estimates by broken
patchwise equilibration for the curl–curl problem. Math. Comp. 91, 333
(2022), 37–74. Journal version, preprint .
16. Chaumont-Frelet, T., and Vohralík, M. Equivalence of local-best and
global-best approximations in H(curl). Calcolo 58 (2021), 53. Journal
version, free view-only version, preprint .
17. Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M.
Post-processing of the planewave approximation of Schrödinger equations.
Part I: linear operators. IMA J. Numer. Anal. 41, 4 (2021), 2423–2455.
Journal version, preprint .
18. Chaumont-Frelet, T., Ern, A., and Vohralík, M. On the derivation
of guaranteed and p-robust a posteriori error estimates for the Helmholtz
equation. Numer. Math. 148, 3 (2021), 525–573. Journal version, preprint .
19. Miraçi, A., Papež, J., and Vohralík, M. A-posteriori-steered p-robust
multigrid with optimal step-sizes and adaptive number of smoothing steps.
SIAM J. Sci. Comput. 43, 5 (2021), S117–S145. Journal version, paper .
20. Haberl, A., Praetorius, D., Schimanko, S., and Vohralík, M.
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear
operators including iterative linearization and algebraic solver. Numer.
Math. 147, 3 (2021), 679–725. Journal version, preprint .
21. Miraçi, A., Papež, J., and Vohralík, M. Contractive local adaptive
smoothing based on Dörfler’s marking in a-posteriori-steered p-robust
multigrid solvers. Comput. Methods Appl. Math. 21, 2 (2021), 445–468.
Journal version, preprint .
22. Cancčs, C., Nabet, F., and Vohralík, M. Convergence and a posteriori
error analysis for energy-stable finite element approximations of degenerate
parabolic equations. Math. Comp. 90, 328 (2021), 517–563. Journal version,
preprint .
23. Ern, A., Vohralík, M., and Zakerzadeh, M. Guaranteed and robust
L2-norm a posteriori error estimates for 1D linear advection problems.
ESAIM Math. Model. Numer. Anal. 55 (2021), S447–S474. Journal version,
preprint .
24. Chaumont-Frelet, T., Ern, A., and Vohralík,
M. Polynomial-degree-robust H(curl)-stability of discrete minimization in
a tetrahedron. C. R. Math. Acad. Sci. Paris 358, 9–10 (2020), 1101–1110.
Journal version, preprint .
25. Miraçi, A., Papež, J., and Vohralík, M. A multilevel algebraic error
estimator and the corresponding iterative solver with p-robust behavior.
SIAM J. Numer. Anal. 58, 5 (2020), 2856–2884. Journal version, paper .
26. Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík,
M. Guaranteed a posteriori bounds for eigenvalues and eigenvectors:
multiplicities and clusters. Math. Comp. 89, 326 (2020), 2563–2611. Journal
version, preprint .
27. Papež, J., Rüde, U., Vohralík, M., and Wohlmuth, B. Sharp algebraic
and total a posteriori error bounds for h and p finite elements via a multilevel
approach. Recovering mass balance in any situation. Comput. Methods Appl.
Mech. Engrg. 371 (2020), 113243. Journal version, preprint .
28. Dabaghi, J., Martin, V., and Vohralík, M. Adaptive inexact semismooth
Newton methods for the contact problem between two membranes. J. Sci.
Comput. 84 (2020), 28. Journal version, preprint .
29. Smears, I., and Vohralík, M. Simple and robust equilibrated flux a
posteriori estimates for singularly perturbed reaction–diffusion problems.
ESAIM Math. Model. Numer. Anal. 54, 6 (2020), 1951–1973. Journal
version, preprint .
30. Blechta, J., Málek, J., and Vohralík, M. Localization of the W-1,q norm
for local a posteriori efficiency. IMA J. Numer. Anal. 40, 2 (2020), 914–950.
Journal version, preprint .
31. Dabaghi, J., Martin, V., and Vohralík, M. A posteriori estimates
distinguishing the error components and adaptive stopping criteria for
numerical approximations of parabolic variational inequalities. Comput.
Methods Appl. Mech. Engrg. 367 (2020), 113105. Journal version, preprint .
32. Ern, A., and Vohralík, M. Stable broken H1 and H(div) polynomial
extensions for polynomial-degree-robust potential and flux reconstruction
in three space dimensions. Math. Comp. 89, 322 (2020), 551–594. Journal
version, preprint .
33. Ben Gharbia, I., Dabaghi, J., Martin, V., and Vohralík, M. A
posteriori error estimates for a compositional two-phase flow with nonlinear
complementarity constraints. Comput. Geosci. 24 (2020), 1031–1055.
Journal version, preprint .
34. Daniel, P., Ern, A., and Vohralík, M. An adaptive hp-refinement
strategy with inexact solvers and computable guaranteed bound on the error
reduction factor. Comput. Methods Appl. Mech. Engrg. 359 (2020), 112607.
Journal version, preprint .
35. Mallik, G., Vohralík, M., and Yousef, S. Goal-oriented a posteriori error
estimation for conforming and nonconforming approximations with inexact
solvers. J. Comput. Appl. Math. 366 (2020), 112367. Journal version,
preprint .
36. Ahmed, E., Ali Hassan, S., Japhet, C., Kern, M., and Vohralík, M.
A posteriori error estimates and stopping criteria for space-time domain
decomposition for two-phase flow between different rock types. SMAI J.
Comput. Math. 5 (2019), 195–227. Journal version, preprint .
37. Ern, A., Smears, I., and Vohralík, M. Equilibrated flux a posteriori
error estimates in L2(H1)-norms for high-order discretizations of parabolic
problems. IMA J. Numer. Anal. 39, 3 (2019), 1158–1179. Journal version,
preprint .
38. Ciarlet, Jr., P., and Vohralík, M. Localization of global norms
and robust a posteriori error control for transmission problems with
sign-changing coefficients. ESAIM Math. Model. Numer. Anal. 52, 5 (2018),
2037–2064. Journal version, preprint .
39. Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M.
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and
eigenvectors: a unified framework. Numer. Math. 140, 4 (2018), 1033–1079.
Journal version, preprint .
40. Daniel, P., Ern, A., Smears, I., and Vohralík, M. An adaptive
hp-refinement strategy with computable guaranteed bound on the error
reduction factor. Comput. Math. Appl. 76, 5 (2018), 967–983. Journal
version, preprint .
41. Ali Hassan, S., Japhet, C., and Vohralík, M. A posteriori stopping
criteria for space-time domain decomposition for the heat equation in mixed
formulations. Electron. Trans. Numer. Anal. 49 (2018), 151–181. Journal
version, preprint .
42. Ali Hassan, S., Japhet, C., Kern, M., and Vohralík, M. A posteriori
stopping criteria for optimized Schwarz domain decomposition algorithms in
mixed formulations. Comput. Methods Appl. Math. 18, 3 (2018), 495–519.
Journal version, preprint .
43. Čermák, M., Hecht, F., Tang, Z., and Vohralík, M. Adaptive
inexact iterative algorithms based on polynomial-degree-robust a posteriori
estimates for the Stokes problem. Numer. Math. 138, 4 (2018), 1027–1065.
Journal version, free view-only version, preprint .
44. Papež, J., Strakoš, Z., and Vohralík, M. Estimating and localizing
the algebraic and total numerical errors using flux reconstructions. Numer.
Math. 138, 3 (2018), 681–721. Journal version, free view-only version,
preprint .
45. Vohralík, M., and Yousef, S. A simple a posteriori estimate on general
polytopal meshes with applications to complex porous media flows. Comput.
Methods Appl. Mech. Engrg. 331 (2018), 728–760. Journal version, preprint
.
46. Ern, A., Smears, I., and Vohralík, M. Guaranteed, locally space-time
efficient, and polynomial-degree robust a posteriori error estimates for
high-order discretizations of parabolic problems. SIAM J. Numer. Anal.
55, 6 (2017), 2811–2834. Journal version, paper .
47. Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M.
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and
eigenvectors: conforming approximations. SIAM J. Numer. Anal. 55, 5
(2017), 2228–2254. Journal version, paper .
48. Ern, A., Smears, I., and Vohralík, M. Discrete p-robust H(div)-liftings
and a posteriori estimates for elliptic problems with H-1 source terms.
Calcolo 54, 3 (2017), 1009–1025. Journal version, free view-only version,
preprint .
49. Dolejší, V., Ern, A., and Vohralík, M. hp-adaptation driven by
polynomial-degree-robust a posteriori error estimates for elliptic problems.
SIAM J. Sci. Comput. 38, 5 (2016), A3220–A3246. Journal version, paper
.
50. Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M. A
perturbation-method-based post-processing for the planewave discretization
of Kohn–Sham models. J. Comput. Phys. 307 (2016), 446–459. Journal
version, preprint .
51. Ern, A., and Vohralík, M. Polynomial-degree-robust a posteriori
estimates in a unified setting for conforming, nonconforming, discontinuous
Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53, 2 (2015),
1058–1081. Journal version, paper .
52. Di Pietro, D. A., Vohralík, M., and Yousef, S. Adaptive regularization,
linearization, and discretization and a posteriori error control for the
two-phase Stefan problem. Math. Comp. 84, 291 (2015), 153–186. Journal
version, preprint .
53. Di Pietro, D. A., Vohralík, M., and Yousef, S. An a posteriori-based,
fully adaptive algorithm with adaptive stopping criteria and mesh
refinement for thermal multiphase compositional flows in porous media.
Comput. Math. Appl. 68, 12 B (2014), 2331–2347. Journal version, preprint
.
54. Cancčs, E., Dusson, G., Maday, Y., Stamm, B., and Vohralík, M.
A perturbation-method-based a posteriori estimator for the planewave
discretization of nonlinear Schrödinger equations. C. R. Math. Acad. Sci.
Paris 352, 11 (2014), 941–946. Journal version, preprint .
55. Dolejší, V., Šebestová, I., and Vohralík, M. Algebraic and discretization
error estimation by equilibrated fluxes for discontinuous Galerkin methods
on nonmatching grids. J. Sci. Comput. 64, 1 (2015), 1–34. Journal version,
preprint .
56. Di Pietro, D. A., Flauraud, E., Vohralík, M., and Yousef, S. A
posteriori error estimates, stopping criteria, and adaptivity for multiphase
compositional Darcy flows in porous media. J. Comput. Phys. 276 (2014),
163–187. Journal version, preprint .
57. Di Pietro, D. A., and Vohralík, M. A review of recent advances in
discretization methods, a posteriori error analysis, and adaptive algorithms
for numerical modeling in geosciences. Oil & Gas Science and Technology
69, 4 (2014), 701–729. Journal version, paper .
58. Cancčs, C., Pop, I. S., and Vohralík, M. An a posteriori error
estimate for vertex-centered finite volume discretizations of immiscible
incompressible two-phase flow. Math. Comp. 83, 285 (2014), 153–188.
Journal version, preprint .
59. Vohralík, M., and Wheeler, M. F. A posteriori error estimates, stopping
criteria, and adaptivity for two-phase flows. Comput. Geosci. 17, 5 (2013),
789–812. Journal version, preprint .
60. Ern, A., and Vohralík, M. Adaptive inexact Newton methods with
a posteriori stopping criteria for nonlinear diffusion PDEs. SIAM J. Sci.
Comput. 35, 4 (2013), A1761–A1791. Journal version, paper .
61. Dolejší, V., Ern, A., and Vohralík, M. A framework for robust a
posteriori error control in unsteady nonlinear advection-diffusion problems.
SIAM J. Numer. Anal. 51, 2 (2013), 773–793. Journal version, paper .
62. Pencheva, G. V., Vohralík, M., Wheeler, M. F., and Wildey, T. Robust
a posteriori error control and adaptivity for multiscale, multinumerics, and
mortar coupling. SIAM J. Numer. Anal. 51, 1 (2013), 526–554. Journal
version, paper .
63. Ern, A., and Vohralík, M. Four closely related equilibrated flux
reconstructions for nonconforming finite elements. C. R. Math. Acad. Sci.
Paris 351, 1-2 (2013), 77–80. Journal version, preprint .
64. Ern, A., and Vohralík, M. Adaptive inexact Newton methods: a posteriori error control and speedup of calculations. SIAM News 46, 1 (2013), 1,4.
65. Vohralík, M., and Wohlmuth, B. I. Mixed finite element methods:
implementation with one unknown per element, local flux expressions,
positivity, polygonal meshes, and relations to other methods. Math. Models
Methods Appl. Sci. 23, 5 (2013), 803–838. Journal version, preprint .
66. Vohralík, M., and Wohlmuth, B. I. From face to element unknowns by
local static condensation with application to nonconforming finite elements.
Comput. Methods Appl. Mech. Engrg. 253 (2013), 517–529. Journal version,
preprint .
67. Hannukainen, A., Stenberg, R., and Vohralík, M. A unified framework
for a posteriori error estimation for the Stokes problem. Numer. Math. 122,
4 (2012), 725–769. Journal version, preprint .
68. Ben Belgacem, F., Bernardi, C., Blouza, A., and Vohralík, M. On the
unilateral contact between membranes. Part 2: A posteriori analysis and
numerical experiments. IMA J. Numer. Anal. 32, 3 (2012), 1147–1172.
Journal version, preprint .
69. Hilhorst, D., and Vohralík, M. A posteriori error estimates for combined
finite volume–finite element discretizations of reactive transport equations
on nonmatching grids. Comput. Methods Appl. Mech. Engrg. 200, 5-8
(2011), 597–613. Journal version, preprint .
70. Vohralík, M. Guaranteed and fully robust a posteriori error estimates
for conforming discretizations of diffusion problems with discontinuous
coefficients. J. Sci. Comput. 46, 3 (2011), 397–438. Journal version, preprint
.
71. El Alaoui, L., Ern, A., and Vohralík, M. Guaranteed and robust a
posteriori error estimates and balancing discretization and linearization
errors for monotone nonlinear problems. Comput. Methods Appl. Mech.
Engrg. 200, 37-40 (2011), 2782–2795. Journal version, preprint .
72. Jiránek, P., Strakoš, Z., and Vohralík, M. A posteriori error estimates
including algebraic error and stopping criteria for iterative solvers. SIAM
J. Sci. Comput. 32, 3 (2010), 1567–1590. Journal version, paper .
73. Vohralík, M. Unified primal formulation-based a priori and a posteriori
error analysis of mixed finite element methods. Math. Comp. 79, 272 (2010),
2001–2032. Journal version, preprint .
74. Ern, A., and Vohralík, M. A posteriori error estimation based on
potential and flux reconstruction for the heat equation. SIAM J. Numer.
Anal. 48, 1 (2010), 198–223. Journal version, paper .
75. Ern, A., Stephansen, A. F., and Vohralík, M. Guaranteed
and robust discontinuous Galerkin a posteriori error estimates for
convection-diffusion-reaction problems. J. Comput. Appl. Math. 234, 1
(2010), 114–130. Journal version, preprint .
76. Eymard, R., Hilhorst, D., and Vohralík, M. A combined finite
volume–finite element scheme for the discretization of strongly nonlinear
convection–diffusion–reaction problems on nonmatching grids. Numer.
Methods Partial Differential Equations 26, 3 (2010), 612–646. Journal
version, preprint .
77. Cheddadi, I., Fučík, R., Prieto, M. I., and Vohralík, M. Guaranteed
and robust a posteriori error estimates for singularly perturbed
reaction-diffusion problems. M2AN Math. Model. Numer. Anal. 43, 5
(2009), 867–888. Journal version, preprint .
78. Ern, A., and Vohralík, M. Flux reconstruction and a posteriori error
estimation for discontinuous Galerkin methods on general nonmatching
grids. C. R. Math. Acad. Sci. Paris 347, 7-8 (2009), 441–444. Journal
version, preprint .
79. Ben Belgacem, F., Bernardi, C., Blouza, A., and Vohralík, M. On the
unilateral contact between membranes. Part 1: Finite element discretization
and mixed reformulation. Math. Model. Nat. Phenom. 4, 1 (2009), 21–43.
Journal version, preprint .
80. Ben Belgacem, F., Bernardi, C., Blouza, A., and Vohralík, M. A finite
element discretization of the contact between two membranes. M2AN Math.
Model. Numer. Anal. 43, 1 (2009), 33–52. Journal version, preprint .
81. Vohralík, M. Residual flux-based a posteriori error estimates for finite
volume and related locally conservative methods. Numer. Math. 111, 1
(2008), 121–158. Journal version, preprint .
82. Vohralík, M. A posteriori error estimation in the conforming
finite element method based on its local conservativity and using local
minimization. C. R. Math. Acad. Sci. Paris 346, 11-12 (2008), 687–690.
Journal version, preprint .
83. Ern, A., Nicaise, S., and Vohralík, M. An accurate H(div)
flux reconstruction for discontinuous Galerkin approximations of elliptic
problems. C. R. Math. Acad. Sci. Paris 345, 12 (2007), 709–712. Journal
version, preprint .
84. Vohralík, M. A posteriori error estimates for lowest-order mixed finite
element discretizations of convection-diffusion-reaction equations. SIAM J.
Numer. Anal. 45, 4 (2007), 1570–1599. Journal version, paper .
85. Vohralík, M., Maryška, J., and Severýn, O. Mixed and nonconforming
finite element methods on a system of polygons. Appl. Numer. Math. 57, 2
(2007), 176–193. Journal version, preprint .
86. Eymard, R., Hilhorst, D., and Vohralík, M. A combined finite
volume–nonconforming/mixed-hybrid finite element scheme for degenerate
parabolic problems. Numer. Math. 105, 1 (2006), 73–131. Journal version,
preprint .
87. Vohralík, M. Equivalence between lowest-order mixed finite element
and multi-point finite volume methods on simplicial meshes. M2AN Math.
Model. Numer. Anal. 40, 2 (2006), 367–391. Journal version, preprint .
88. Vohralík, M. On the discrete Poincaré–Friedrichs inequalities for
nonconforming approximations of the Sobolev space H1. Numer. Funct.
Anal. Optim. 26, 7-8 (2005), 925–952. Journal version, preprint .
89. Vohralík, M. Equivalence between mixed finite element and multi-point
finite volume methods. C. R. Math. Acad. Sci. Paris 339, 7 (2004), 525–528.
Journal version, preprint .
90. Maryška, J., Severýn, O., and Vohralík, M. Numerical simulation of
fracture flow with a mixed-hybrid FEM stochastic discrete fracture network
model. Comput. Geosci. 8, 3 (2004), 217–234. Journal version, preprint .
91. Ern, A., Guzmán, J., Potu, P., and Vohralík, M. Local L2-bounded
commuting projections using discrete local problems on Alfeld splits. HAL
Preprint 04931497, submitted for publication, 2025. .
92. Bastidas Olivares, M., Beni Hamad, A., Vohralík, M., and Yotov,
I. A posteriori algebraic error estimates and nonoverlapping domain
decomposition in mixed formulations: energy coarse grid balancing, local
mass conservation on each step, and line search. HAL Preprint 04843665,
submitted for publication, 2024. .
93. Ern, A., Guzmán, J., Potu, P., and Vohralík, M. Discrete Poincaré
inequalities: a review on proofs, equivalent formulations, and behavior of
constants. HAL Preprint 04837821, submitted for publication, 2024. .
94. Miraçi, A., Papež, J., Vohralík, M., and Yotov, I. A-posteriori-steered
p-robust multigrid and domain decomposition methods with optimal
step-sizes for mixed finite element discretizations of elliptic problems. HAL
Preprint 04611932, submitted for publication, 2024. .
95. Harnist, A., Mitra, K., Rappaport, A., and Vohralík, M. Robust
augmented energy a posteriori estimates for Lipschitz and strongly
monotone elliptic problems. HAL Preprint 04033438, 2024. .
96. Demkowicz, L., and Vohralík, M. p-robust equivalence of global
continuous constrained and local
discontinuous unconstrained approximation, a p-stable local commuting
projector, and optimal elementwise hp approximation estimates in H(div).
HAL Preprint 04503603, submitted for publication, 2024. .
97. Vohralík, M. p-robust equivalence of global continuous and local
discontinuous approximation, a p-stable local projector, and optimal
elementwise hp approximation estimates in H1. HAL Preprint 04436063,
submitted for publication, 2024. .
98. Mitra, K., and Vohralík, M. Guaranteed, locally efficient, and robust
a posteriori estimates for nonlinear elliptic problems in iteration-dependent
norms. An orthogonal decomposition result based on iterative linearization.
HAL Preprint 04156711, submitted for publication, 2023. .