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

Total Cost €


EC-Contrib. €






 GATIPOR project word cloud

Explore the words cloud of the GATIPOR project. It provides you a very rough idea of what is the project "GATIPOR" about.

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Project "GATIPOR" data sheet

The following table provides information about the project.


Organization address
postcode: 78153

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Project website
 Total cost 1˙283˙087 €
 EC max contribution 1˙283˙087 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2020-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Efficient use of computational resources with a reliable outcome is a definite target in numerical simulations of partial differential equations (PDEs). Although this has been an important subject of numerical analysis and scientific computing for decades, still, surprisingly, often more than 90% of the CPU time in numerical simulations is literally wasted and the accuracy of the final outcome is not guaranteed. The reason is that addressing this complex issue rigorously is extremely challenging, as it stems from linking several rather disconnected domains like modeling, analysis of PDEs, numerical analysis, numerical linear algebra, and scientific computing. The goal of this project is to design novel inexact algebraic and linearization solvers, with each step being adaptively steered by optimal (guaranteed and robust) a posteriori error estimates, thus online interconnecting all parts of the numerical simulation of complex environmental porous media flows. The key novel ingredients will be multilevel algebraic solvers, tailored to porous media simulations, with problem- and discretization-dependent restriction, prolongation, and smoothing, yielding mass balance on all grid levels, accompanied by local adaptive stopping criteria. We shall theoretically prove the convergence of the new algorithms and justify their optimality, with in particular guaranteed (without any unknown constant) error reduction and overall computational load. Implementation into established numerical simulation codes and assessment on renowned academic and industrial benchmarks will consolidate the theoretical results. As a final outcome, the total simulation error will be certified and current computational burden cut by orders of magnitude. This would represent a cardinal technological advance both theoretically as well as practically in urgent environmental applications, namely the nuclear waste storage and the geological sequestration of CO2.


year authors and title journal last update
List of publications.
2017 Ahmed , Elyes; Ali Hassan , Sarah; Japhet , Caroline; Kern , Michel; Vohralík , Martin
A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types
published pages: , ISSN: , DOI:
HAL Preprints 2019-05-31
2017 Alexandre Ern, Iain Smears, Martin Vohralík
Discrete p-robust $$varvec{H}({{mathrm{div}}})$$ H ( div ) -liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ H - 1 source terms
published pages: 1009-1025, ISSN: 0008-0624, DOI: 10.1007/s10092-017-0217-4
Calcolo 54/3 2019-05-31
2017 Papež , Jan; Rüde , Ulrich; Vohralík , Martin; Wohlmuth , Barbara
Sharp algebraic and total a posteriori error bounds for $h$ and $p$ finite elements via a multilevel approach
published pages: , ISSN: , DOI:
HAL Preprints 2019-05-31
2018 Málek, Josef; Vohralík, Martin; Blechta, Jan
Localization of the $W^{-1,q}$ norm for local a posteriori efficiency
published pages: , ISSN: , DOI:
HAL Preprints 2019-05-31
2017 Dabaghi , Jad; Martin , Vincent; Vohralík , Martin
Adaptive inexact semismooth Newton methods for the contact problem between two membranes
published pages: , ISSN: , DOI:
HAL Preprints 2019-05-31
2017 Alexandre Ern, Iain Smears, Martin Vohralík
Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems
published pages: 2811-2834, ISSN: 0036-1429, DOI: 10.1137/16M1097626
SIAM Journal on Numerical Analysis 55/6 2019-05-31
2018 Patrik Daniel, Alexandre Ern, Iain Smears, Martin Vohralík
An adaptive h p -refinement strategy with computable guaranteed bound on the error reduction factor
published pages: 967-983, ISSN: 0898-1221, DOI: 10.1016/j.camwa.2018.05.034
Computers & Mathematics with Applications 76/5 2019-05-31
2016 Ern, Alexandre; Vohralík, Martin; Dolejší, Vít
hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems
published pages: A3220–A3246, ISSN: 1064-8275, DOI: 10.1137/15M1026687
SIAM Journal on Scientific Computing 38/5 2019-05-31
2018 Sarah Ali Hassan, Caroline Japhet, Michel Kern, Martin Vohralík
A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations
published pages: 495-519, ISSN: 1609-4840, DOI: 10.1515/cmam-2018-0010
Computational Methods in Applied Mathematics 18/3 2019-05-31
2018 Martin Vohralík, Soleiman Yousef
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows
published pages: 728-760, ISSN: 0045-7825, DOI: 10.1016/j.cma.2017.11.027
Computer Methods in Applied Mechanics and Engineering 331 2019-05-31
2018 Patrick Ciarlet, Jr., Martin Vohralik
Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients
published pages: , ISSN: 0764-583X, DOI: 10.1051/m2an/2018034
ESAIM: Mathematical Modelling and Numerical Analysis 2019-05-31
2018 Vohralík, Martin; Ern, Alexandre
Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions
published pages: , ISSN: , DOI:
HAL Preprints 2019-05-31
2018 Alexandre Ern, Iain Smears, Martin Vohralík
Equilibrated flux a posteriori error estimates in $L^2(H^1)$-norms for high-order discretizations of parabolic problems
published pages: , ISSN: 0272-4979, DOI: 10.1093/imanum/dry035
IMA Journal of Numerical Analysis 2019-05-31
2018 Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework
published pages: 1033-1079, ISSN: 0029-599X, DOI: 10.1007/s00211-018-0984-0
Numerische Mathematik 140/4 2019-05-31
2018 Sarah Ali Hassan, Caroline Japhet, Martin Vohralík
A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations
published pages: 151-181, ISSN: 1068-9613, DOI: 10.1553/etna_vol49s151
ETNA - Electronic Transactions on Numerical Analysis 49 j 2019-05-31
2018 Martin Čermák, Frédéric Hecht, Zuqi Tang, Martin Vohralík
Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem
published pages: 1027-1065, ISSN: 0029-599X, DOI: 10.1007/s00211-017-0925-3
Numerische Mathematik 138/4 2019-05-31
2018 J. Papež, Z. Strakoš, M. Vohralík
Estimating and localizing the algebraic and total numerical errors using flux reconstructions
published pages: 681-721, ISSN: 0029-599X, DOI: 10.1007/s00211-017-0915-5
Numerische Mathematik 138/3 2019-05-31
2017 Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík
Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations
published pages: 2228-2254, ISSN: 0036-1429, DOI: 10.1137/15M1038633
SIAM Journal on Numerical Analysis 55/5 2019-05-31
2018 Cancès, Clément; Nabet, Flore; Vohralík, Martin
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations
published pages: , ISSN: , DOI:
2018 Neumuller, Martin; Smears, Iain
Time-parallel iterative solvers for parabolic evolution equations
published pages: , ISSN: , DOI:

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