The convergence of Rothe's method for parabolic differential equations
type: Item
instance of: scholarly article
title: The convergence of Rothe's method for parabolic differential equations
zbMATH Open document ID: 0681.65085
DOI: 10.4171/ZAA/272
author: Yanyan Li
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1987-01-01T00:00:00Z
review text: The convergence of the full discretization scheme (time discretized Galerkin method is proved for the nonlinear evolution equation \[ u_ t(x,t)+\sum_{| i| \leq m}(-1)^{| i|}D^ iA_ i(x,t,Du)=f(x,t) \] with Dirichlet boundary conditions under monotonicity and coerciveness assumptions on A(x,t,s) in s and polynomial growth conditions. The corresponding system of algebraic equations is nonlinear. The convergence is obtained in the space \(L_{\infty}(0,T;L_ 2(\Omega))\).
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 4115892
zbMATH Keywords: Rothe's method
zbMATH Keywords: stability
zbMATH Keywords: consistency
zbMATH Keywords: convergence
zbMATH Keywords: full discretization scheme
zbMATH Keywords: time discretized Galerkin method
zbMATH Keywords: nonlinear evolution equation
reviewed by: Jozef Kacur
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4115892