Average case complexity of elliptic partial differential equations
type: Item
instance of: scholarly article
title: Average case complexity of elliptic partial differential equations
zbMATH Open document ID: 0685.65095
DOI: 10.1016/0885-064X(89)90028-9
published in: Journal of Complexity
publication date: 1989-01-01T00:00:00Z
review text: The author obtains tight complexity bounds for the approximate solution of elliptic partial differential equations in the worst case setting, and finds conditions that are necessary and sufficient for the finite element method to be an almost optimal complexity algorithm. Since these bounds show that elliptic partial differential equations are intractable in the worst case setting, it is natural to seek another setting in which partial differential equations are tractable. With this in mind, the author looks at the average case setting. Moreover, the author shows that the finite element method with properly chosen parameters is an almost optimal complexity algorithm in the average case.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 68Q25
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4123225
zbMATH Keywords: worst case setting
zbMATH Keywords: finite element method
zbMATH Keywords: almost optimal complexity algorithm
zbMATH Keywords: average case setting
author: A. G. Werschulz
reviewed by: Zhanyuan Hou
MaRDI profile type: Publication
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full work available at URL: 0885-064x(89)90028-9
OpenAlex ID: W2046296184
description: scientific article; zbMATH DE number 4123225