Splitting extrapolation based on domain decomposition for finite element approximations
type: Item
instance of: scholarly article
title: Splitting extrapolation based on domain decomposition for finite element approximations
zbMATH Open document ID: 0949.65120
DOI: 10.1007/BF02916946
author: Tao Lü
author: Yong Feng
published in: Science in China. Series E
publication date: 2000-12-05T00:00:00Z
review text: The authors study a method called splitting extrapolation which is meant to be a competitive algorithm for large scale problems. Advantages of domain decomposition and sparse-grid methods are combined with high accuracy. The method applies to elliptic second-order problems, linear and nonlinear, and eigenvalue problems, in two and three space dimensions. Large scale problems are decomposed into many smaller discrete problems which can be solved in parallel. Multivariate asymptotic expansions of finite element errors are exploited. In Section 1 three theorems -- one for each type of problem -- are formulated, giving the form of the expansion. Sections 2 through 4 contain the proofs. Sections 5 and 6 contain details of the algorithm and examples in three dimensions with known analytical solutions.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1066763
zbMATH Keywords: error bounds
zbMATH Keywords: parallel algorithms
zbMATH Keywords: splitting extrapolation
zbMATH Keywords: algorithm
zbMATH Keywords: large scale problems
zbMATH Keywords: domain decomposition
zbMATH Keywords: sparse-grid methods
zbMATH Keywords: elliptic second-order problems
zbMATH Keywords: linear
zbMATH Keywords: nonlinear
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: finite element
reviewed by: Kurt Frischmuth
MaRDI profile type: Publication
cites work: Q3685932
cites work: Q3677101
cites work: The Splitting Extrapolation Method
full work available at URL: https://doi.org/10.1007/bf02916946
OpenAlex ID: W1993105366
description: scientific article; zbMATH DE number 1066763