A holomorphic semigroup approach to the lumped mass finite element method
type: Item
instance of: scholarly article
title: A holomorphic semigroup approach to the lumped mass finite element method
zbMATH Open document ID: 1058.65108
author: Norikazu Saito
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-16T00:00:00Z
review text: The lumped mass finite element discretization of parabolic equations replaces the functions in the variational form with the time derivative by its lumped counterparts. Optimal error estimates in \(L^2(\Omega)\) and \(H^1(\Omega)\) using this discretization for linear homogeneous parabolic equations are presented where the second order partial differential operator is strongly elliptic. The domain is assumed to be a convex polyhedron in \(\mathbb{R}^d\), \(d\in\{1,2,3\}\). The continuous-in-time formulation of the equation is considered and linear finite elements are used as discretization in space. Results for finite element discretizations without lumping are generalized. The error estimates are derived using the holomorphic semigroup theory.
reviewed by: Volker John
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2091426
zbMATH Keywords: finite element method
zbMATH Keywords: lumped mass approximation
zbMATH Keywords: holomorphic semigroup
zbMATH Keywords: parabolic equations
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: j.cam.2003.11.003
OpenAlex ID: W2019368384
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DOI: 10.1016/J.CAM.2003.11.003
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description: scientific article; zbMATH DE number 2091426