Analysis of an algorithm for generating locally optimal meshes for approximation by discontinuous piecewise polynomials |
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Authors: | Y Tourigny M J Baines |
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Institution: | School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom ; Department of Mathematics, University of Reading, P.O. Box 220, Reading RG6 6AF, United Kingdom |
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Abstract: | This paper discusses the problem of constructing a locally optimal mesh for the best approximation of a given function by discontinuous piecewise polynomials. In the one-dimensional case, it is shown that, under certain assumptions on the approximated function, Baines' algorithm M.J. Baines, Math. Comp., 62 (1994), pp. 645-669] for piecewise linear or piecewise constant polynomials produces a mesh sequence which converges to an optimal mesh. The rate of convergence is investigated. A two-dimensional modification of this algorithm is proposed in which both the nodes and the connection between the nodes are self-adjusting. Numerical results in one and two dimensions are presented. |
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Keywords: | $L_2$ approximation discontinuous piecewise polynomials adjustable nodes grid generation triangulation |
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