Some error estimates for the lumped mass finite element method for a parabolic problem

DOI10.1090/S0025-5718-2011-02503-2zbMath1251.65129MaRDI QIDQ3117199

Raytcho D. Lazarov, Vidar Thomée, Panagiotis Chatzipantelidis

Publication date: 17 February 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Galerkin methodheat equationerror estimatessemidiscretizationbackward Euler methodCrank-Nicolson methodslumped mass methodnonsmooth initial data

Mathematics Subject Classification ID

Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (10)

A discrete commutator theory for the consistency and phase error analysis of semi-discrete \(C^0\) finite element approximations to the linear transport equation ⋮ The lumped mass FEM for a time-fractional cable equation ⋮ Two time-stepping schemes for sub-diffusion equations with singular source terms ⋮ A Quadratic Finite Volume Method for Parabolic Problems ⋮ Reprint of ``Domain decomposition multigrid methods for nonlinear reaction-diffusion problems ⋮ Weak Galerkin method with \((r, r - 1, r - 1)\)-order finite elements for second order parabolic equations ⋮ Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview ⋮ The lumped mass finite element method for surface parabolic problems: error estimates and maximum principle ⋮ Domain decomposition multigrid methods for nonlinear reaction-diffusion problems ⋮ Error analysis of a FVEM for fractional order evolution equations with nonsmooth initial data

Cites Work

• Parabolic finite element equations in nonconvex polygonal domains
• A holomorphic semigroup approach to the lumped mass finite element method
• The lumped mass finite element method for a parabolic problem
• Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
• Galerkin Finite Element Methods for Parabolic Problems
• Smoothing of initial data and rates of convergence for parabolic difference equations
• Unnamed Item

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