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Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. (English) Zbl 1038.65096
Summary: We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinuities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting discontinuities in such variables as density or entropy, limiting may be applied only in these regions; thereby, preserving a high order of accuracy in regions where solutions are smooth. Several one- and two-dimensional flow problems illustrate the performance of these approaches.

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
Full Text: DOI
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