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). DOI 10.1007/s10208-024-09674-7. Preprint .

3.   Chaumont-Frelet, T., and Vohralík, M. A stable local commuting projector and optimal hp approximation estimates in H(curl). Numer. Math. (2024). DOI 10.1007/s00211-024-01431-w. 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.   Cancès, 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.   Cancès, 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.   Cancès, 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.   Cancès, 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.   Cancès, 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.   Cancès, 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.   Cancès, 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.   Cancès, 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.   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. .

92.   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. .

93.   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. .

94.   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. .

95.   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. .