The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods

DOI10.1016/j.crma.2011.09.005zbMath1230.65122OpenAlexW2059466979MaRDI QIDQ643611

Assyr Abdulle, Gilles Vilmart

Publication date: 2 November 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://archive-ouverte.unige.ch/unige:41942

zbMATH Keywords

finite element methodnumerical quadraturea priori error estimateshomogenization methodssecond-order quasilinear elliptic problems

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Quasilinear elliptic equations (35J62)

Related Items (6)

COUPLING HETEROGENEOUS MULTISCALE FEM WITH RUNGE–KUTTA METHODS FOR PARABOLIC HOMOGENIZATION PROBLEMS: A FULLY DISCRETE SPACETIME ANALYSIS ⋮ Reduced-order modelling numerical homogenization ⋮ A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems ⋮ Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems ⋮ Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems ⋮ A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift

Cites Work

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• A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems
• Finite element solution of nonlinear elliptic problems
• On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type
• Analysis of the heterogeneous multiscale method for elliptic homogenization problems
• A Galerkin Method for a Nonlinear Dirichlet Problem
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM

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