Sobolev regularity estimation for hp-adaptive finite element methods

P. Houston, B. Senior and E. Süli
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P. Houston: University of Leicester, Department of Mathematics and Computer Science
B. Senior: University of Leicester, Department of Mathematics and Computer Science
E. Süli: University of Oxford, Computing Laboratory

A chapter in Numerical Mathematics and Advanced Applications, 2003, pp 631-656 from Springer

Abstract: Summary In this paper we develop an algorithm for estimating the local Sobolev regularity index of a given function by monitoring the decay rate of its Legendre expansion coefficients. On the basis of these local regularities, we design and implement an hp-adaptive finite element method based on employing discontinuous piecewise polynomials, for the approximation of nonlinear systems of hyperbolic conservation laws. The performance of the proposed adaptive strategy is demonstrated numerically.

Keywords: Posteriori Error; Dual Solution; Posteriori Error Estimation; Spectral Element Method; Regularity Estimation (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2089-4_58

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DOI: 10.1007/978-88-470-2089-4_58

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