Adaptive Grid Conference Edinburgh 96: ainsworth Abstract

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Adaptive HP finite element methods: theory, practice and parallelism

M Ainsworth

Mathematics Department
Leicester University
Leicester LE1 7RH, UK.
ain@mcs.le.ac.uk

Abstract

The talk will survey theoretical work by the author on a posteriori error estimators and domain decomposition methods for HP finite element methods for elliptic systems. (The HP version of the finite element method achieves convergence by not only refining the mesh adaptively but also adaptively enriching the spectral order of the approximation.)

The a posteriori error estimators (developed with J.T. Oden) are inexpensive to compute, based on independent local computations over small patches of elements. Their key theoretical property is that they provide sharp, guaranteed upper bounds on the error in energy.

The domain decomposition algorithms are in the spirit of methods due to Bramble, Pasciak and Schwatz and Mandel but apply to full HP finite element approximation. Theory shows that the growth of the condition number is logarithmic in the order P and the number of elements in each subdomain.

Both the estimator and the DD algorithm were developed with parallelism and highly refined meshes with non-uniform spectral orders in mind. Numerical examples will be given confirming that the methods can be implemented in parallel and provide effective algorithms in practice.

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Last modified Fri Jun 21 19:19:09 GB-Eire 1996 (DBD)