A priori \(L^2\) error analysis for an expanded mixed finite element method for quasilinear pseudo-parabolic equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1285.65060
DOI: 10.4134/JKMS.2014.51.1.067
published in: Journal of the Korean Mathematical Society
publication date: 2014-01-21T00:00:00Z
full work available at URL: http://www.mathnet.or.kr/mathnet/kms_content.php
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 6248006
zbMATH Keywords: quasilinear pseudo-parabolic equation
zbMATH Keywords: semidiscrete approximation
zbMATH Keywords: expanded mixed finite element method
zbMATH Keywords: \(L^2\) optimal convergence
MaRDI profile type: Publication
title: A priori \(L^2\) error analysis for an expanded mixed finite element method for quasilinear pseudo-parabolic equations
author: Mi Ray Ohm
author: Hyunyoung Lee
author: Jun Yong Shin
review text: The authors consider a quasilinear pseudo-parabolic equation (in which the flux contains nonlinearities and the time derivative of the gradient of the solution) in a convex \(d\)-dimensional domain (\(1\leq d\leq 3\)) along with second-kind boundary and initial data in Sobolev spaces \(W^{s,p}\) for the space variables at \(L^2\) spaces in time. Assuming smooth nonlinearities and a Lipschitz-continuous right hand side, they use a regular quasi-uniform grid to discretize the space variables by finite elements. Solving for the solution, its gradient and the flux, they need 3 different functions and discretization spaces and a corresponding expanded mixed finite element weak formulation. For this, they prove existence of the semidiscrete solution by reformulating the task as a fixed point problem and using the Brouwer existence theorem. Further, they prove the convergence of the semidiscrete solution being optimal with respect to smoothness, polynomial degree and dimension \(d\).
reviewed by: Gisbert Stoyan
description: scientific article; zbMATH DE number 6248006