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A posteriori error estimates for elliptic boundary-value problems

Part of: Partial differential equations, boundary value problems Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

W. L. Chan
W. L. Chan
Affiliation:
Department of Mathematics Science CentreThe Chinese University of Hong Kong Shatin, N. T., Hong Kong
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Abstract

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A posteriori error estimates for a class of elliptic unilateral boundary value problems are obtained for functions satisfying only part of the boundary conditions. Next, we give an alternative approach to the a posteriori error estimates for self-adjoint boundary value problems developed by Aubin and Burchard. Further, we are able to construct an alternative estimate with mild additional assumptions. An example of a linear differential operator of order 2k is given.

MSC classification

Secondary: 35J30: Higher-order elliptic equations 35J35: Variational methods for higher-order elliptic equations 35J40: Boundary value problems for higher-order elliptic equations 65N15: Error bounds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 159 - 168
Copyright
Copyright © Australian Mathematical Society 1985

References

Aubin, J. P. (1972), Approximation of elliptic boundary-value problems, (Wiley Interscience, New York).Google Scholar
Aubin, J. P. and Burchard, H. (1971), ‘Some aspects of the method of the hypercircle applied to elliptic variational problems’, Proceedings of SYNSPADE, edited Hubbard, B. (Academic Press, New York).Google Scholar
Lions, J. L. and Stampacchia, G. (1967), ‘Variational inequalities’, Comm. Pure Appl. Math. 20, 493–519.CrossRefGoogle Scholar