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A posteriori subcell finite volume limiter for general $$P_NP_M$$ schemes: applications from gasdynamics to relativistic magnetohydrodynamics. (English) Zbl 07352182
The authors propose a new simple, robust, accurate and computationally efficient limiting strategy for the general family of ADER $$P_NP_M$$ schemes, allowing the use of hybrid reconstructed methods ($$N > 0$$, $$M > N$$ ) in the modeling of discontinuous phenomena. This new approach has been applied to many different systems of hyperbolic conservation laws, providing highly accurate numerical results in all cases. The performance of the class of intermediate $$P_N P_M$$ schemes with $$M > N > 0$$ is compared with pure the Discontinuous Galerkin (DG) schemes ($$M = N$$). It is remarked that in the most cases the intermediate $$P_N P_M$$ schemes lead to reduced computational cost compared with the pure DG methods. A new efficient posteriori subcell finite volume limiting strategy that is valid for the entire class of $$P_NP_M$$ schemes is presented.
##### MSC:
 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 76N15 Gas dynamics (general theory) 76W05 Magnetohydrodynamics and electrohydrodynamics 76Y05 Quantum hydrodynamics and relativistic hydrodynamics