Split least-squares finite element methods for linear and nonlinear parabolic problems

Authors:
Hongxing Rui;Sang Dong Kim;Seokchan Kim
Affiliations:
School of Mathematics, Shandong University, Jinan, Shandong, 250100, China;Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea;Department of Applied Mathematics, Changwon National University, Changwon 641-773, South Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 9
Cited 1

First-order system least squares for second-order partial differential equations: part I

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Least-squares mixed finite elements for second-order elliptic problems

SIAM Journal on Numerical Analysis
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II

SIAM Journal on Numerical Analysis
Least-Squares Finite Element Approximations to Solutions of Interface Problems

SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Least-Squares Galerkin Methods for Parabolic Problems I: Semidiscretization in Time

SIAM Journal on Numerical Analysis
Least-Squares Galerkin Methods for Parabolic Problems II: The Fully Discrete Case and Adaptive Algorithms

SIAM Journal on Numerical Analysis
On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles

SIAM Journal on Numerical Analysis
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

A remark on least-squares Galerkin procedures for pseudohyperbolic equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we propose some least-squares finite element procedures for linear and nonlinear parabolic equations based on first-order systems. By selecting the least-squares functional properly each proposed procedure can be split into two independent symmetric positive definite sub-procedures, one of which is for the primary unknown variable u and the other is for the expanded flux unknown variable @s. Optimal order error estimates are developed. Finally we give some numerical examples which are in good agreement with the theoretical analysis.