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Explicit finite element methods for symmetric hyperbolic equations. (English) Zbl 0923.65065

Authors’ abstract: A family of explicit space-time finite element methods for the initial boundary value problem for linear, symmetric hyperbolic systems of equations is described and analyzed. The method generalizes the discontinuous Galerkin method and, as is typical for this method, obtains error estimates of order \(O(h^{n+1/2})\) for approximations by polynomials of degree \(\leq n\).

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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