Publications in international journals
Martin Vohralík


Papers published or accepted for publication

2017

1.   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. (2017). Accepted for publication. Preprint PDF icon.

2.   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. (2017). DOI 10.1007/s00211-017-0925-3. Preprint PDF icon.

3.   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. (2017). DOI 10.1137/16M1097626. Preprint PDF icon.

4.   Papež, J., Strakoš, Z., and Vohralík, M. Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Numer. Math. (2017). DOI 10.1007/s00211-017-0915-5. Journal version, free view-only version, preprint PDF icon.

5.   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 PDF icon.

6.   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 PDF icon.

2016

7.   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 PDF icon.

8.   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 PDF icon.

2015

9.   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. PDF icon.

10.   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 PDF icon.

2014

11.   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 PDF icon.

12.   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 PDF icon.

13.   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 PDF icon.

14.   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 PDF icon.

15.   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 PDF icon.

16.   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 PDF icon.

2013

17.   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 PDF icon.

18.   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 PDF icon.

19.   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 PDF icon.

20.   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 PDF icon.

21.   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 PDF icon.

22.   Ern, A., and Vohralík, M. Adaptive inexact Newton methods: a posteriori error control and speedup of calculations. SIAM News 46, 1 (2013), 1,4.

23.   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 PDF icon.

24.   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 PDF icon.

2012

25.   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 PDF icon.

26.   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 PDF icon.

2011

27.   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 PDF icon.

28.   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 PDF icon.

29.   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 PDF icon.

2004–2010

30.   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 PDF icon.

31.   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 PDF icon.

32.   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 PDF icon.

33.   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 PDF icon.

34.   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 PDF icon.

35.   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 PDF icon.

36.   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 PDF icon.

37.   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 PDF icon.

38.   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 PDF icon.

39.   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 PDF icon.

40.   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 PDF icon.

41.   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 PDF icon.

42.   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 PDF icon.

43.   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 PDF icon.

44.   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 PDF icon.

45.   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 PDF icon.

46.   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 PDF icon.

47.   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 PDF icon.

48.   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 PDF icon.

Papers submitted

49.   Blechta, J., Málek, J., and Vohralík, M. Localization of the W-1,q norm for local a posteriori efficiency. HAL Preprint 01332481, submitted for publication, 2016. PDF icon.

50.   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. HAL Preprint 01422204, submitted for publication, 2016. PDF icon.

51.   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. HAL Preprint 01483461, submitted for publication, 2017. PDF icon.

52.   Ern, A., Smears, I., and Vohralík, M. Equilibrated flux a posteriori error estimates in L2(H1)-norms for high-order discretizations of parabolic problems. HAL Preprint 01489721, submitted for publication, 2017. PDF icon.

53.   Ali Hassan, S., Japhet, C., Kern, M., and Vohralík, M. A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations. HAL Preprint 01529532, submitted for publication, 2017. PDF icon.

54.   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. HAL Preprint 01540956, submitted for publication, 2017. PDF icon.

55.   Ciarlet, Jr., P., and Vohralík, M. Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients. HAL Preprint 01148476v2, submitted for publication, 2017. PDF icon.

56.   Ali Hassan, S., Japhet, C., and Vohralík, M. A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations. HAL Preprint 01586862, submitted for publication, 2017. PDF icon.