Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in \(L^1\)

DOI10.1007/s00211-006-0033-2zbMath1144.65072OpenAlexW2012797268MaRDI QIDQ861655

Vivette Girault, Juan Casado-Díaz, Tómas Chacón-Rebollo, Macarena Gómez-Mármol, François Murat

Publication date: 30 January 2007

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-006-0033-2

zbMATH Keywords

finite elementerror estimatedivergence formsecond order linear elliptic equationsright-hand side in \(L^1(\Omega)\)

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

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Cites Work

• Approximated solutions of equations with \(L^ 1\) data. Application to the \(H\)-convergence of quasilinear parabolic equations
• Nonlinear elliptic and parabolic equations involving measure data
• Regularity results for discrete solutions of second order elliptic problems in the finite element method
• Convergence of linear finite elements for diffusion equations with measure data.
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Maximum principle and uniform convergence for the finite element method
• Finite element convergence for singular data
• Nonlinear Elliptic Equations with Right Hand Side Measures
• Une remarque sur l'unicité des solutions pour l'opérateur de Serrin
• A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data
• Failure of the discrete maximum principle for an elliptic finite element problem
• FINITE ELEMENT APPROXIMATIONS FOR THE LAPLACE OPERATOR WITH A RIGHT-HAND SIDE MEASURE
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