Parallel, adaptive finite element methods for conservation laws
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).
scientific article; zbMATH DE number 609622
scientific article