On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach-Reference-Cited by-同舟云学术

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

Published:1981 Issue:156 Volume:37 Page:361-384
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Vogelius M.,Babuška I.

Abstract

This paper is the last in a series of three which analyze an adaptive approximate approach for solving ( n + 1 ) (n + 1) -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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1981-37-156/S0025-5718-1981-0628701-7/S0025-5718-1981-0628701-7.pdf

Reference7 articles.

1. Reliable error estimation and mesh adaptation for the finite element method;Babuška, Ivo,1980

2. Nonlinear semigroups and differential equations in Banach spaces

3. V. Dunder & S. Ridlon, "Practical applications of the finite element method," ASCE J. Structures Division ST1, January 1978, pp. 9-21.

4. N. Dunford & J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.

5. M. Vogelius, Ph.D. Thesis, University of Maryland, December 1979.

Cited by 45 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation;Advances in Computational Mathematics;2024-07-16

2. Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity;Encyclopedia of Computational Mechanics Second Edition;2017-12-18

3. Plates and Shells: Asymptotic Expansions and Hierarchical Models;Encyclopedia of Computational Mechanics Second Edition;2017-12-15

4. HiMod Reduction of Advection–Diffusion–Reaction Problems with General Boundary Conditions;Journal of Scientific Computing;2017-11-24

5. Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniques;ESAIM: Mathematical Modelling and Numerical Analysis;2017-02-24