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.
CITATION STYLE
Houston, P., Senior, B., & Süli, E. (2003). Sobolev regularity estimation for hp-adaptive finite element methods. In Numerical Mathematics and Advanced Applications (pp. 631–656). Springer Milan. https://doi.org/10.1007/978-88-470-2089-4_58
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