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A second order explicit finite element scheme to multi-dimensional conservation laws and its convergence. (English) Zbl 0999.65105
Summary: 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 in \(L^2\) is proved under a stronger condition, \(\Delta t\leq Ch^{4/3}\).

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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