A direct global superconvergence analysis for Sobolev and viscoelasticity type equations
type: Item
instance of: scholarly article
title: A direct global superconvergence analysis for Sobolev and viscoelasticity type equations
zbMATH Open document ID: 0902.65034
DOI: 10.1023/A:1022288409629
published in: Applications of Mathematics
publication date: 1998-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/32965
review text: The first part of the paper contains a numerical analysis of a superconvergence phenomenon which arises when solving an evolution partial differential equation of Sobolev type by the finite element method. The authors prove a global superconvergence over a rectangular domain provided the true solution is sufficiently smooth. A similar technique is used to prove a global superconvergence for a viscoelasticity type evolution equation. Continuous and piecewise bilinear functions are employed over uniform partitions.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 74Hxx
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 1203974
zbMATH Keywords: viscoelasticity type equations
zbMATH Keywords: global superconvergence
zbMATH Keywords: Sobolev equation
zbMATH Keywords: finite element method
zbMATH Keywords: evolution equation
author: Qun Lin
author: Shuhua Zhang
reviewed by: Michal Křížek
MaRDI profile type: Publication
cites work: Superconvergence of a Finite Element Approximation to the Solution of a Sobolev Equation in a Single Space Variable
cites work: The Approximation of Certain Parabolic Equations Backward in Time by Sobolev Equations
cites work: Numerical Solution of Sobolev Partial Differential Equations
cites work: Galerkin approximations to nonlinear pseudo-parabolic partial differential equations
cites work: Stability and Convergence of Difference Approximations to Pseudo-Parabolic Partial Differential Equations
cites work: Uniform Error Estimates for Difference Approximations to NonLinear Pseudo-Parabolic Partial Differential Equations
cites work: An immediate analysis for global superconvergence for integrodifferential equations
cites work: Q3361840
cites work: Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions
cites work: Ritz–Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations
cites work: Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension
cites work: Error estimates for a Galerkin method for a class of model equations for long waves
cites work: A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
OpenAlex ID: W184775003
description: scientific article; zbMATH DE number 1203974