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Parallel, adaptive finite element methods for conservation laws. (English) Zbl 0826.65084
The authors explore extensively how to numerically solve hyperbolic conservation laws by means of nonconforming finite elements; computations are to be carried on parallel computers and a significant set of examples in one and two dimensions is analyzed, with an explicit Runge-Kutta method being employed for time discretization. In this way, discontinuities that may develop with time in hyperbolic phenomena are implicit in the discretization from the onset. Adaptive \(h\)- and \(p\)- refinements are shown to provide accuracy at low computational cost, when compared with fixed meshes computations. The paper sets the lines for further developments combining both types of refinement, in order “to optimize computational work in both smooth and discontinuous solution regions” (sic).

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
35L65 Hyperbolic conservation laws
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