Analysis of a Quadratic Finite Element Method for Second-Order Linear Elliptic PDE, With Low Regularity Data

DOI10.1080/01630563.2019.1663432zbMath1436.65186OpenAlexW2973816358MaRDI QIDQ4959901

Rachid Messaoudi, Abdeluaab Lidouh, Belkassem Seddoug

Publication date: 7 April 2020

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2019.1663432

zbMATH Keywords

error estimatequadratic finite elementrenormalized solutiondiagonally dominant matrix\(L^1\)-data

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order elliptic equations (35J15) PDEs with measure (35R06)

Cites Work

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• Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in \(L^1\)
• Nonlinear elliptic and parabolic equations involving measure data
• Failure of the discrete maximum principle for an elliptic finite element problem
• A version of Simpson's rule for multiple integrals

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