Guaranteed fully adaptive algorithms with tailored inexact solvers for complex porous media flows

Publications

Peer reviewed articles (40)

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

Author(s): Alexander Haberl, Dirk Praetorius, Stefan Schimanko, Martin Vohralík
Published in: Numerische Mathematik, 147/3, 2021, Page(s) 679-725, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-021-01176-w

Equivalence of local-best and global-best approximations in H(curl)

Author(s): Chaumont-Frelet, Théophile; Vohralík, Martin
Published in: Calcolo, 2021, ISSN 1126-5434
Publisher: Springer Nature Switzerland AG
DOI: 10.1007/s10092-021-00430-9

A-Posteriori-Steered $p$-Robust Multigrid with Optimal Step-Sizes and Adaptive Number of Smoothing Steps

Author(s): Ani Miraçi, Jan Papež, Martin Vohralík
Published in: SIAM Journal on Scientific Computing, 2021, Page(s) S117-S145, ISSN 1064-8275
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1349503

Contractive local adaptive smoothing based on Dörfler marking in a-posteriori-steered $p$-robust multigrid solvers

Author(s): Ani Miraçi; Jan Papež; Martin Vohralík
Published in: Computational Methods in Applied Mathematics, 21/2, 2021, Page(s) 445-468, ISSN 1609-9389
Publisher: De Gruyter
DOI: 10.1515/cmam-2020-0024

Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations

Author(s): Clément Cancès, Flore Nabet, Martin Vohralík
Published in: Mathematics of Computation, 90/328, 2021, Page(s) 517-563, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3577

Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H (div)

Author(s): Alexandre Ern, Thirupathi Gudi, Iain Smears, Martin Vohralík
Published in: IMA Journal of Numerical Analysis, 2021, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/draa103

Guaranteed and robust L 2 -norm a posteriori error estimates for 1D linear advection problems

Author(s): Alexndre Ern, Martin Vohralík, Mohammad Zakerzadeh
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 55, 2021, Page(s) S447-S474, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2020041

On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation

Author(s): T. Chaumont-Frelet, A. Ern, M. Vohralík
Published in: Numerische Mathematik, 148/3, 2021, Page(s) 525-573, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-021-01192-w

A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities

Author(s): Jad Dabaghi, Vincent Martin, Martin Vohralík
Published in: Computer Methods in Applied Mechanics and Engineering, 367, 2020, Page(s) 113105, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113105

Adaptive Inexact Semismooth Newton Methods for the Contact Problem Between Two Membranes

Author(s): Jad Dabaghi, Vincent Martin, Martin Vohralík
Published in: Journal of Scientific Computing, 84/2, 2020, Page(s) 28, ISSN 0885-7474
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-020-01264-3

Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters

Author(s): Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík
Published in: Mathematics of Computation, 89/326, 2020, Page(s) 2563-2611, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3549

A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows

Author(s): Martin Vohralík, Soleiman Yousef
Published in: Computer Methods in Applied Mechanics and Engineering, 331, 2018, Page(s) 728-760, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2017.11.027

An adaptive h p -refinement strategy with computable guaranteed bound on the error reduction factor

Author(s): Patrik Daniel, Alexandre Ern, Iain Smears, Martin Vohralík
Published in: Computers & Mathematics with Applications, 76/5, 2018, Page(s) 967-983, ISSN 0898-1221
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.camwa.2018.05.034

Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients

Author(s): Patrick Ciarlet, Jr., Martin Vohralik
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 2018, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2018034

A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations

Author(s): Sarah Ali Hassan, Caroline Japhet, Martin Vohralík
Published in: ETNA - Electronic Transactions on Numerical Analysis, 49 journal refereed 28, 2018, Page(s) 151-181, ISSN 1068-9613
Publisher: Kent State University
DOI: 10.1553/etna_vol49s151

A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations

Author(s): Sarah Ali Hassan, Caroline Japhet, Michel Kern, Martin Vohralík
Published in: Computational Methods in Applied Mathematics, 18/3, 2018, Page(s) 495-519, ISSN 1609-4840
Publisher: Walter de Gruyter and Co.
DOI: 10.1515/cmam-2018-0010

A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types

Author(s): Elyes Ahmed, Sarah Ali Hassan, Caroline Japhet, Michel Kern, Martin Vohralík
Published in: The SMAI journal of computational mathematics, 5, 2019, Page(s) 195-227, ISSN 2426-8399
Publisher: SMAI Journal of Computational Mathematics
DOI: 10.5802/smai-jcm.47

Discrete p-robust $$\varvec{H}({{\mathrm{div}}})$$ H ( div )

Author(s): Alexandre Ern, Iain Smears, Martin Vohralík
Published in: Calcolo, 54/3, 2017, Page(s) 1009-1025, ISSN 0008-0624
Publisher: Springer Verlag
DOI: 10.1007/s10092-017-0217-4

Time-Parallel Iterative Solvers for Parabolic Evolution Equations

Author(s): Martin Neumüller, Iain Smears
Published in: SIAM Journal on Scientific Computing, 41/1, 2019, Page(s) C28-C51, ISSN 1064-8275
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1172466

Estimating and localizing the algebraic and total numerical errors using flux reconstructions

Author(s): J. Papež, Z. Strakoš, M. Vohralík
Published in: Numerische Mathematik, 138/3, 2018, Page(s) 681-721, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-017-0915-5

Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems

Author(s): Alexandre Ern, Iain Smears, Martin Vohralík
Published in: SIAM Journal on Numerical Analysis, 55/6, 2017, Page(s) 2811-2834, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/16M1097626

Equilibrated flux a posteriori error estimates in $L^2(H^1)$-norms for high-order discretizations of parabolic problems

Author(s): Alexandre Ern, Iain Smears, Martin Vohralík
Published in: IMA Journal of Numerical Analysis, 39, 2018, Page(s) 1158–1179, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/dry035

Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations

Author(s): Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík
Published in: SIAM Journal on Numerical Analysis, 55/5, 2017, Page(s) 2228-2254, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/15M1038633

hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems

Author(s): Ern, Alexandre; Vohralík, Martin; Dolejší, Vít
Published in: SIAM Journal on Scientific Computing, 38/5, 2016, Page(s) A3220–A3246, ISSN 1064-8275
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/15M1026687

Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework

Author(s): Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík
Published in: Numerische Mathematik, 140/4, 2018, Page(s) 1033-1079, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-018-0984-0

Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem

Author(s): Martin Čermák, Frédéric Hecht, Zuqi Tang, Martin Vohralík
Published in: Numerische Mathematik, 138/4, 2018, Page(s) 1027-1065, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-017-0925-3

Stable broken $H^1$ and $H(\mathrm {div})$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions

Author(s): Alexandre Ern, Martin Vohralík
Published in: Mathematics of Computation, 89/322, 2020, Page(s) 551-594, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3482

Localization of the $W^{-1,q}$ norm for local a posteriori efficiency

Author(s): Jan Blechta, Josef Málek, Martin Vohralík
Published in: IMA Journal of Numerical Analysis, 2019, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drz002

A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities

Author(s): Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
Published in: Computer Methods in Applied Mechanics and Engineering, 2020, ISSN 0045-7825
Publisher: Elsevier BV

A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints

Author(s): Ibtihel Ben Gharbia, Jad Dabaghi, Vincent Martin, Martin Vohralík
Published in: Computational Geosciences, 2020, ISSN 1420-0597
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10596-019-09909-5

Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters

Author(s): Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
Published in: Mathematics of Computation, 2020, ISSN 0025-5718
Publisher: American Mathematical Society

Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers

Author(s): Gouranga Mallik, Martin Vohralík, Soleiman Yousef
Published in: Journal of Computational and Applied Mathematics, 366, 2020, Page(s) 112367, ISSN 0377-0427
Publisher: Elsevier BV
DOI: 10.1016/j.cam.2019.112367

An adaptive h p -refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor

Author(s): Patrik Daniel, Alexandre Ern, Martin Vohralík
Published in: Computer Methods in Applied Mechanics and Engineering, 359, 2020, Page(s) 112607, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2019.112607

Post-processing of the planewave approximation of Schrödinger equations. Part I: linear operators

Author(s): Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík
Published in: IMA Journal of Numerical Analysis, 2020, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/draa044

Polynomial-degree-robust H ( curl ) -stability of discrete minimization in a tetrahedron

Author(s): Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
Published in: Comptes Rendus. Mathématique, 358/9-10, 2020, Page(s) 1101-1110, ISSN 1778-3569
Publisher: Académie des sciences
DOI: 10.5802/crmath.133

Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems

Author(s): Iain Smears, Martin Vohralík
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 54/6, 2020, Page(s) 1951-1973, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2020034

Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations

Author(s): Jan Papež, Martin Vohralík
Published in: Numerical Algorithms, 2021, ISSN 1017-1398
Publisher: Baltzer Science Publishers B.V.
DOI: 10.1007/s11075-021-01118-5

A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with $p$-Robust Behavior

Author(s): Ani Miraçi, Jan Papež, Martin Vohralík
Published in: SIAM Journal on Numerical Analysis, 58/5, 2020, Page(s) 2856-2884, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1275929

Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem

Author(s): Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
Published in: Mathematics of Computation, 2021, ISSN 1088-6842
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3673

Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation

Author(s): Jan Papež, Ulrich Rüde, Martin Vohralík, Barbara Wohlmuth
Published in: Computer Methods in Applied Mechanics and Engineering, 371, 2020, Page(s) 113243, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113243

Other (19)

Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: adaptivity and inexact resolution

Author(s): Ben Gharbia, Ibtihel; Ferzly, Joëlle; Vohralík, Martin; Yousef, Soleiman
Published in: 2021
Publisher: HAL Preprints Open Archive

Guaranteed contraction of adaptive inexact $hp$-refinement strategies with realistic stopping criteria

Author(s): Patrik Daniel, Martin Vohralík
Published in: 2021
Publisher: HAL Preprints Open Archive

A posteriori error estimates for the Richards equation

Author(s): Koondanibha Mitra, Martin Vohralík
Published in: 2021
Publisher: HAL Preprints Open Archive

Adaptive inexact semismooth Newton methods for the contact problem between two membranes

Author(s): Dabaghi , Jad; Martin , Vincent; Vohralík , Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

Sharp algebraic and total a posteriori error bounds for $h$ and $p$ finite elements via a multilevel approach. Recovering mass balance in any situation

Author(s): Papež, Jan; Rüde, Ulrich; Vohralík, Martin; Wohlmuth, Barbara
Published in: 2019
Publisher: HAL Preprints Open Archive

Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations

Author(s): Cancès, Clément; Nabet, Flore; Vohralík, Martin
Published in: 2018
Publisher: HAL Preprints Open Archive

Guaranteed and robust $L_2$-norm a posteriori error estimates for 1D linear advection problems

Author(s): Ern, Alexandre; Vohralík, Martin; Zakerzadeh, Mohammad
Published in: 2020
Publisher: HAL Preprints Open Archive

On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation

Author(s): Chaumont-Frelet, Théophile; Ern, Alexandre; Vohralík, Martin
Published in: 2019
Publisher: HAL Preprints Open Archive

Guaranteed contraction of adaptive inexact $hp$-refinement strategies with realistic stopping criteria

Author(s): Daniel, Patrik; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div)

Author(s): Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin
Published in: 2019
Publisher: HAL Preprints Open Archive

Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems

Author(s): Smears, Iain; Vohralík, Martin
Published in: 2018
Publisher: HAL Preprints Open Archive

Contractive local adaptive smoothing based on Dörfler marking in a-posteriori-steered $p$-robust multigrid solvers

Author(s): Miraçi, Ani; Papež, Jan; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations

Author(s): Papež, Jan; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

A posteriori-steered $p$-robust multigrid with optimal step-sizes and adaptive number of smoothing steps

Author(s): Miraçi, Ani; Papež, Jan; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

A multilevel algebraic error estimator and the corresponding iterative solver with $p$-robust behavior

Author(s): Miraçi, Ani; Papež, Jan; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

"Post-processing of the planewave approximation of Schr\""odinger equations. Part I: linear operators"

Author(s): Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

Author(s): Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin
Published in: 2020
Publisher: HAL Preprints Open Archive

p-robust equilibrated flux reconstruction in H(curl) based on local minimizations. Application to a posteriori analysis of the curl-curl problem

Author(s): Chaumont-Frelet, Théophile; Vohralík, Martin
Published in: 2021
Publisher: HAL Preprints Open Archive

A space-time multiscale mortar mixed finite element method for parabolic equations

Author(s): Jayadharan, Manu; Kern, Michel; Vohralík, Martin; Yotov, Ivan
Published in: 2021
Publisher: HAL Preprints Open Archive

Thesis dissertations (5)

A-posteriori-steered and adaptive $p$-robust multigrid solvers

Author(s): Ani Miraçi
Published in: Numerical Analysis [math.NA]. Sorbonne Université; INRIA Paris, 2019. English, 14/12/2020, 2020
Publisher: HAL Preprints Open Archive

A posteriori error estimates for variational inequalities: application to a two-phase flow in porous media

Author(s): Jad Dabaghi
Published in: Numerical Analysis [math.NA]. Sorbonne Université; INRIA Paris, 2019. English, 03/06/2019, 2019
Publisher: HAL Preprints Open Archive

A posteriori error estimates for variational inequalities: application to a two-phase flow in porous media

Author(s): Dabaghi, Jad
Published in: Numerical Analysis [math.NA]. Sorbonne Université, 2019. English, 2019
Publisher: HAL Preprints Open Archive

Adaptive hp-finite elements with guaranteed error contraction and inexact multilevel solvers

Author(s): Daniel, Patrik
Published in: Numerical Analysis [math.NA]. Sorbonne Université; INRIA Paris, 2019. English, 2019
Publisher: HAL Preprints Open Archive

Adaptive hp-finite elements with guaranteed error contraction and inexact multilevel solvers

Author(s): Patrik Daniel
Published in: Numerical Analysis [math.NA]. Sorbonne Université; INRIA Paris, 2019. English, 22/03/2019, 2019
Publisher: HAL Preprints Open Archive