Skip to main content

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

Searching for OpenAIRE data...

Publications

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

Author(s): Dabaghi , Jad; Martin , Vincent; Vohralík , Martin
Published in: 2020

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

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

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

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

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

Author(s): Daniel, Patrik; Vohralík, Martin
Published in: 2020

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

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

Author(s): Smears, Iain; Vohralík, Martin
Published in: 2018

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

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

Author(s): Papež, Jan; Vohralík, Martin
Published in: 2020

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

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

"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

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

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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
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

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
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
DOI: 10.1016/j.cma.2019.112607

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

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