Error estimates of the lumped mass finite element method for semilinear elliptic problems

DOI10.1016/j.cam.2011.11.009zbMath1275.65076OpenAlexW2136356251MaRDI QIDQ2428114

Haixiong Yu, Jin-ping Zeng

Publication date: 24 April 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.11.009

zbMATH Keywords

numerical resultssemilinear elliptic problemcascadic multigrid method\(L^{2}\)-error estimatelumped mass discretization

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61)

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Cites Work

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• Semilinear elliptic equations for beginners. Existence results via the variational approach
• A rectangular finite volume element method for a semilinear elliptic equation
• On the convergence of a cascadic multigrid method for semilinear elliptic problem
• Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem
• A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes
• A lumped mass finite element method for vibration analysis of elastic plate-plate structures
• Finite element solution of nonlinear elliptic problems
• Finite element approximations applied to the nonlinear boundary value problem \(\Delta(u)=b(u)^2\)
• Schwarz algorithm for the solution of variational inequalities with nonlinear source terms
• The cascadic multigrid method for elliptic problems
• Some estimates of the rate of convergence for the cascadic conjugate-gradient method
• A cascadic multigrid algorithm for semilinear indefinite elliptic problems
• A cascadic multigrid algorithm for semilinear elliptic problems
• A new cascadic multigrid
• Economical cascadic multigrid method (ECMG)
• An \(L^{\infty}\)-error estimate for finite element solution of nonlinear elliptic problem with a source term
• A finite volume element method for a non‐linear elliptic problem
• Mixed Finite Element Methods for Quasilinear Second-Order Elliptic Problems
• The lumped mass finite element method for a parabolic problem
• A multilevel successive iteration method for nonlinear elliptic problems
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Mixed Finite Element Methods for Nonlinear Second-Order Elliptic Problems
• Parallel solutions of variational inequality problems with nonlinear source terms