High order schemes for hyperbolic problems using globally continuous approximation and avoiding mass matrices

R Abgrall (1)

1 UZH - Universität Zürich [Zürich] = University of Zurich

When integrating unsteady problems using globally continuous representation of the solution, as for continuous finite element methods, one faces the problem of inverting a mass matrix. In some cases, one has to recompute this mass matrix at each time steps. In some other methods that are not directly formulated by standard variational principles, it is not clear how to write an invertible mass matrix. Hence, in this paper, we show how to avoid this problem for hyperbolic systems, and we also detail the conditions under which this is possible. Analysis and simulation support our conclusions, namely that it is possible to avoid inverting mass matrices without sacrificing the accuracy of the scheme. This paper is an extension of [4] and [26].

Mots clés: hyperbolic problems; unsteady problems; finite element; mass matrix

Domaines: Mathématiques [math]

R Abgrall. High order schemes for hyperbolic problems using globally continuous approximation and avoiding mass matrices. 2017. ⟨hal-01445543v2⟩