Construction of conservative PkPm space-time residual discretizations for conservation laws I : theoretical aspects
作者： Adam Larat , Mario Ricchiuto
DOI:
关键词: High order 、 Space (mathematics) 、 Mathematics 、 Nonlinear system 、 Upwind scheme 、 Residual 、 Courant–Friedrichs–Lewy condition 、 Mathematical analysis 、 Conservation law 、 Space time
摘要: This paper deals with the construction of conservative high order and positivity preserving schemes for nonlinear hyperbolic conservation laws. In particular, we consider space-time Petrov-Galerkin discretizations inspired by residual distribution ideas based on a PkPm polynomial approximations in space-time. The approximation is continuous space discontinuous time so that one single slab at can be dealt with. We show constructions involving linear schemes. Principles borrowed from approach, such as multidimensional upwinding preservation, are used to construct test functions. numerical results dimensional laws higher accuracy obtained uniformly respect physical CFL number.
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