A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
In the field of high-order discontinuous methods for convection dominated problems on unstructured meshes, Runge-Kutta discontinuous Galerkin methods have attracted great interest during the last two decades. The aim of the present paper is to propose a new slope limiter for discontinuous Galerkin methods of any order of accuracy which satisfies certain properties [cf. \textit{B. Cockburn} and \textit{C. W. Shu}, J. Comput. Phys. 141, No. 2, 199-224 (1998; Zbl 0920.65059) and \textit{R. Biswas, K. D. Devine} and \textit{J. E. Flaherty}, Appl. Numer. Math. 14, No. 1-3, 255-283 (1994; Zbl 0826.65084)]. Numerical results illustrate here good behaviour of the proposed limiter, for any kind of solutions (regular or with discontinuities). Extension of the new limiting procedure to triangular meshes, for the set of basis functions of Dubiner and in case of \(P^1\) and \(P^2\) approximations is presented.
Runge-Kutta discontinuous Galerkin methods
scientific article; zbMATH DE number 1610379
scientific article