[Reconstruction du flux et estimations a posteriori pour la méthode de Galerkine discontinue sur des maillages non-coïncidants avec mailles polygonales]
Les méthodes de Galerkine discontinues sont bien adaptées pour traiter des maillages non-coïncidants avec mailles polygonales. Nous présentons dans cette Note une reconstruction
Discontinuous Galerkin methods handle very well general polygonal and nonmatching meshes. We present in this Note a
Accepté le :
Publié le :
@article{CRMATH_2009__347_7-8_441_0, author = {Ern, Alexandre and Vohral{\'\i}k, Martin}, title = {Flux reconstruction and a posteriori error estimation for discontinuous {Galerkin} methods on general nonmatching grids}, journal = {Comptes Rendus. Math\'ematique}, pages = {441--444}, publisher = {Elsevier}, volume = {347}, number = {7-8}, year = {2009}, doi = {10.1016/j.crma.2009.01.017}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.crma.2009.01.017/} }
TY - JOUR AU - Ern, Alexandre AU - Vohralík, Martin TI - Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids JO - Comptes Rendus. Mathématique PY - 2009 SP - 441 EP - 444 VL - 347 IS - 7-8 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2009.01.017/ DO - 10.1016/j.crma.2009.01.017 LA - en ID - CRMATH_2009__347_7-8_441_0 ER -
%0 Journal Article %A Ern, Alexandre %A Vohralík, Martin %T Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids %J Comptes Rendus. Mathématique %D 2009 %P 441-444 %V 347 %N 7-8 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2009.01.017/ %R 10.1016/j.crma.2009.01.017 %G en %F CRMATH_2009__347_7-8_441_0
Ern, Alexandre; Vohralík, Martin. Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 441-444. doi : 10.1016/j.crma.2009.01.017. https://www.numdam.org/articles/10.1016/j.crma.2009.01.017/
[1] A posteriori error estimation for discontinuous Galerkin finite element approximation, SIAM J. Numer. Anal., Volume 45 (2007) no. 4, pp. 1777-1798
[2] M. Ainsworth, R. Rankin, Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes, Research Report 9, University of Strathclyde, 2008
[3] Equilibrated error estimators for discontinuous Galerkin methods, Numer. Methods Partial Differential Equations, Volume 24 (2008) no. 5, pp. 1236-1252
[4] An accurate
[5] A. Ern, A.F. Stephansen, M. Vohralík, Improved energy norm a posteriori error estimation based on flux reconstruction for discontinuous Galerkin methods, HAL Preprint 00193540 version 1 (14-11-2007), 2007
[6] A. Ern, A.F. Stephansen, M. Vohralík, Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection–diffusion–reaction problems, HAL Preprint 00193540, submitted for publication, 2008
[7] A. Ern, A.F. Stephansen, P. Zunino, A discontinuous Galerkin method with weighted averages for advection–diffusion equations with locally small and anisotropic diffusivity, IMA J. Numer. Anal., (electronic), 2008 | DOI
[8] A posteriori error estimators for locally conservative methods of nonlinear elliptic problems, Appl. Numer. Math., Volume 57 (2007) no. 9, pp. 1065-1080
[9] A local a posteriori error estimator based on equilibrated fluxes, SIAM J. Numer. Anal., Volume 42 (2004) no. 4, pp. 1394-1414
- Posteriori error neural network: A recovery type posteriori error estimator based on neural network for diffusion problems, Computers Mathematics with Applications, Volume 143 (2023), p. 169 | DOI:10.1016/j.camwa.2023.05.007
- Numerical comparison of three a posteriori error estimators for nonconforming finite element method, Moroccan Journal of Pure and Applied Analysis, Volume 9 (2023) no. 1, p. 1 | DOI:10.2478/mjpaa-2023-0001
- Reconstruction method of equilibrated flux for a posteriori error estimate of elliptic problems, International Journal of Modeling, Simulation, and Scientific Computing, Volume 13 (2022) no. 06 | DOI:10.1142/s1793962322500519
- Space–time adaptive splitting scheme for the numerical simulation of polycrystallization, Journal of Computational and Applied Mathematics, Volume 404 (2022), p. 113882 | DOI:10.1016/j.cam.2021.113882
- A simple virtual element-based flux recovery on quadtree, Electronic Research Archive, Volume 29 (2021) no. 6, p. 3629 | DOI:10.3934/era.2021054
- An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem, Russian Journal of Numerical Analysis and Mathematical Modelling, Volume 36 (2021) no. 6, p. 313 | DOI:10.1515/rnam-2021-0026
- A New Hybrid Staggered Discontinuous Galerkin Method on General Meshes, Journal of Scientific Computing, Volume 82 (2020) no. 1 | DOI:10.1007/s10915-019-01119-6
- Analysis of an adaptive HDG method for the Brinkman problem, IMA Journal of Numerical Analysis, Volume 39 (2019) no. 3, p. 1502 | DOI:10.1093/imanum/dry031
- A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows, Computer Methods in Applied Mechanics and Engineering, Volume 331 (2018), p. 728 | DOI:10.1016/j.cma.2017.11.027
- Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method, Journal of Scientific Computing, Volume 75 (2018) no. 2, p. 1079 | DOI:10.1007/s10915-017-0575-8
- A residual a posteriori error estimate for the Virtual Element Method, Mathematical Models and Methods in Applied Sciences, Volume 27 (2017) no. 08, p. 1423 | DOI:10.1142/s0218202517500233
- Efficient Equilibrated Flux Reconstruction in High Order Raviart-Thomas Space for Discontinuous Galerkin Methods, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Volume 119 (2017), p. 467 | DOI:10.1007/978-3-319-65870-4_33
- A guaranteed equilibrated error estimator for the
and magnetodynamic harmonic formulations of the Maxwell system, IMA Journal of Numerical Analysis (2016), p. drw026 | DOI:10.1093/imanum/drw026 - A Posteriori Error Estimate for a PDE-Constrained Optimization Formulation for the Flow in DFNs, SIAM Journal on Numerical Analysis, Volume 54 (2016) no. 1, p. 242 | DOI:10.1137/15m1014760
- Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids, Journal of Scientific Computing, Volume 64 (2015) no. 1, p. 1 | DOI:10.1007/s10915-014-9921-2
- Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes, Journal of Scientific Computing, Volume 64 (2015) no. 2, p. 368 | DOI:10.1007/s10915-014-9937-7
- A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem, Numerical Methods for Partial Differential Equations, Volume 31 (2015) no. 3, p. 950 | DOI:10.1002/num.21929
- Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations, SIAM Journal on Numerical Analysis, Volume 53 (2015) no. 2, p. 1058 | DOI:10.1137/130950100
- Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem, Mathematics of Computation, Volume 84 (2014) no. 291, p. 153 | DOI:10.1090/s0025-5718-2014-02854-8
- Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling, SIAM Journal on Numerical Analysis, Volume 51 (2013) no. 1, p. 526 | DOI:10.1137/110839047
- A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems, SIAM Journal on Numerical Analysis, Volume 51 (2013) no. 2, p. 773 | DOI:10.1137/110859282
- Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics, SIAM Journal on Scientific Computing, Volume 35 (2013) no. 6, p. A2621 | DOI:10.1137/12089973x
- Flux reconstruction for the P2 nonconforming finite element method with application to a posteriori error estimation, Applied Numerical Mathematics, Volume 62 (2012) no. 12, p. 1701 | DOI:10.1016/j.apnum.2012.06.027
- Equilibration techniques for solving contact problems with Coulomb friction, Computer Methods in Applied Mechanics and Engineering, Volume 205-208 (2012), p. 29 | DOI:10.1016/j.cma.2010.12.021
- A unified framework for a posteriori error estimation for the Stokes problem, Numerische Mathematik, Volume 122 (2012) no. 4, p. 725 | DOI:10.1007/s00211-012-0472-x
- Pointwise a Posteriori Error Control for Discontinuous Galerkin Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, Volume 50 (2012) no. 5, p. 2159 | DOI:10.1137/110846397
- Variationally consistent discretization schemes and numerical algorithms for contact problems, Acta Numerica, Volume 20 (2011), p. 569 | DOI:10.1017/s0962492911000079
- Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems, Computer Methods in Applied Mechanics and Engineering, Volume 200 (2011) no. 37-40, p. 2782 | DOI:10.1016/j.cma.2010.03.024
- A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes, Finite Volumes for Complex Applications VI Problems Perspectives, Volume 4 (2011), p. 821 | DOI:10.1007/978-3-642-20671-9_85
- Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients, Journal of Scientific Computing, Volume 46 (2011) no. 3, p. 397 | DOI:10.1007/s10915-010-9410-1
- Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection–diffusion–reaction problems, Journal of Computational and Applied Mathematics, Volume 234 (2010) no. 1, p. 114 | DOI:10.1016/j.cam.2009.12.009
- A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation, SIAM Journal on Numerical Analysis, Volume 48 (2010) no. 1, p. 198 | DOI:10.1137/090759008
Cité par 32 documents. Sources : Crossref