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A second order explicit finite element scheme to multidimensional conservation laws and its convergence

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Abstract

A second order explicit finite element scheme is given for the numerical computation to multi-dimensional scalar conservation laws.L p convergence to entropy solutions is proved under some usual conditions. For two-dimensional problems, uniform mesh, and sufficiently smooth solutions a second order error estimate inL 2 is proved under a stronger condition, Δt≤Ch 2/4

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Ying Long’an

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  1. Ying Long’an
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Correspondence to Ying Long’an.

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Ying, L. A second order explicit finite element scheme to multidimensional conservation laws and its convergence. Sci. China Ser. A-Math. 43, 945–957 (2000). https://doi.org/10.1007/BF02879800

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  • DOI: https://doi.org/10.1007/BF02879800

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