Total flux estimates for a finite element approximation of the Dirichlet problem using the boundary penalty method |
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Authors: | Robert M Shanahan John W Barrett |
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Institution: | (1) Department of Mathematics, Imperial College, SW7 2BZ London, UK |
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Abstract: | Summary This paper considers a fully practical piecewise linear finite element approximation of the Dirichlet problem for a second order self-adjoint elliptic equation,Au=f, in a smooth region<
n
(n=2 or 3) by the boundary penalty method. Using an unfitted mesh; that is
h
, an approximation of with dist (,
h
)Ch
2 is not in general a union of elements; and assuminguH
4 () we show that one can recover the total flux across a segment of the boundary of with an error ofO(h
2). We use these results to study a fully practical piecewise linear finite element approximation of an elliptic equation by the boundary penalty method when the prescribed data on part of the boundary is the total flux.Supported by a SERC research studentship |
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Keywords: | AMS(MOS): 65N30 CR: G1 8 |
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