Residual and hierarchicalaposteriorierror estimates for nonconforming mixed finite element methods

DOI10.1051/m2an:2004044zbMath1077.65113OpenAlexW2116732421MaRDI QIDQ5315490

Linda El Alaoui, Alexandre Ern

Publication date: 8 September 2005

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2004__38_6_903_0

zbMATH Keywords

numerical resultsfinite elementsheterogeneous mediaporous mediaelliptic problemsfinite volumesDarcy flowsDarcy equationsnonconforming methods, a posteriori error estimates

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Flows in porous media; filtration; seepage (76S05) Finite volume methods applied to problems in fluid mechanics (76M12) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

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Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods, Analysis of a finite volume element method for the Stokes problem, Variational multiscale error estimators for the adaptive mesh refinement of compressible flow simulations, A new residual posteriori error estimates of mixed finite element methods for convection‐diffusion‐reaction equations, A uniform additive Schwarz preconditioner for high-order discontinuous Galerkin approximations of elliptic problems, A continuous finite element method with face penalty to approximate Friedrichs' systems, Element boundary terms in reduced order models for flow problems: domain decomposition and adaptive coarse mesh hyper-reduction, Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm, An adaptive finite volume box scheme for solving a class of nonlinear parabolic equations, Variational multiscale error estimators for solid mechanics adaptive simulations: an orthogonal subgrid scale approach, Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations

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