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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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 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

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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 371, 2020, Page(s) 113243, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113243

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

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

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, Issue 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, Issue 03/06/2019, 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, Issue 22/03/2019, 2019
Publisher: HAL Preprints Open Archive

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