ADAPTIVE REMESHING FOR HYPERBOLIC TRANSPORT PROBLEMS

SUMMARY This paper presents an adaptive finite element method for solving scalar hyperbolic transport problems. An equation for the evolution of the error is developed. The Lesaint-Raviart finite element method is used to solve both the transport problem and the error equation. The use of a hierarchical finite element basis on triangles leads to a very efficient error estimation algorithm. The adaptive strategy, based on remeshing, is dmonstrated on several non-trivial problems with known analytical solutions. Higher degree polynomials combined with adaptation produce a very efficient solution algorithm even for problems involving discontinuities.

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