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

Vogelius, M.; Babuška, I.

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

On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach
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by M. Vogelius and I. Babuška PDF

Math. Comp. 37 (1981), 361-384 Request permission

Abstract:

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

References

Ivo Babuška and Werner C. Rheinboldt, Reliable error estimation and mesh adaptation for the finite element method, Computational methods in nonlinear mechanics (Proc. Second Internat. Conf., Univ. Texas, Austin, Tex., 1979) North-Holland, Amsterdam-New York, 1980, pp. 67–108. MR 576902
Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR 0390843

ASCE J. Structures Division ST

Linear Operators

M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions, Math. Comp. 37 (1981), no. 155, 31–46. MR 616358, DOI 10.1090/S0025-5718-1981-0616358-0
M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions, Math. Comp. 37 (1981), no. 155, 31–46. MR 616358, DOI 10.1090/S0025-5718-1981-0616358-0