On a dimensional reduction method a posteriori error estimation and an adaptive approach

M. Vogelius; I. Babuska

doi:10.1090/S0025-5718-1981-0628701-7

On a dimensional reduction method a posteriori error estimation and an adaptive approach

M. Vogelius, I. Babuska

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

This paper is the last in a series of three which analyze an adaptive approximate approach for solving (n + l)-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this paper we show how to find reliable a posteriori estimates for the error and how these can also be used in the design of an adaptive strategy. Various numerical examples are contained in the paper.

Original language	English (US)
Pages (from-to)	361-384
Number of pages	24
Journal	Mathematics of Computation
Volume	37
Issue number	156
DOIs	https://doi.org/10.1090/S0025-5718-1981-0628701-7
State	Published - Oct 1981
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-1981-0628701-7

Cite this

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title = "On a dimensional reduction method a posteriori error estimation and an adaptive approach",

abstract = "This paper is the last in a series of three which analyze an adaptive approximate approach for solving (n + l)-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this paper we show how to find reliable a posteriori estimates for the error and how these can also be used in the design of an adaptive strategy. Various numerical examples are contained in the paper.",

author = "M. Vogelius and I. Babuska",

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AB - This paper is the last in a series of three which analyze an adaptive approximate approach for solving (n + l)-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this paper we show how to find reliable a posteriori estimates for the error and how these can also be used in the design of an adaptive strategy. Various numerical examples are contained in the paper.

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On a dimensional reduction method a posteriori error estimation and an adaptive approach

Abstract

All Science Journal Classification (ASJC) codes

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