Error control for a class of Runge-Kutta discontinuous Galerkin methods for nonlinear conservation laws

被引：31

作者：

Dedner, Andreas

Makridakis, Charalambos

Ohlberger, Mario

机构：

[1] Univ Freiburg, Abt Angew Math, D-79104 Freiburg, Germany

[2] Univ Crete, Dept Appl Math, GR-71409 Iraklion, Greece

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2007年 / 45卷 / 02期

关键词：

discontinuous Galerkin; higher order; adaptive methods; error estimate; finite element;

D O I：

10.1137/050624248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose an a posteriori error estimate for the Runge-Kutta discontinuous Galerkin method (RK-DG) of arbitrary order in arbitrary space dimensions. For stabilization of the scheme a general framework of projections is introduced. Finally it is demonstrated numerically how the a posteriori error estimate is used to design both an efficient grid adaption and gradient limiting strategy. Numerical experiments show the stability of the scheme and the gain in efficiency in comparison with computations on uniform grids.

引用

页码：514 / 538

页数：25

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