THE RUNGE-KUTTA LOCAL PROJECTION RHO-1-DISCONTINUOUS-GALERKIN FINITE-ELEMENT METHOD FOR SCALAR CONSERVATION-LAWS

被引:331
作者
COCKBURN, B [1 ]
SHU, CW [1 ]
机构
[1] UNIV MINNESOTA, INST MATH & APPLICAT, MINNEAPOLIS, MN 55455 USA
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 1991年 / 25卷 / 03期
关键词
D O I
10.1051/m2an/1991250303371
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work we introduce and analyze the model scheme of a new class of methods devised for numerically solving hyperbolic conservation laws. The construction of the scheme is based on a Discontinuous Galerkin finite element space-discretization, combined suitably with a high-order accurate total variation diminishing Runge-Kutta time-discretization, and a local projection which enforces the global stability of the scheme. The resulting scheme verifies a maximum principle, is total variation bounded in the means, linearly stable for CFL is-an-element-of [0, 1/3], and formally uniformly second-order accurate in time and space. Moreover, it converges to a weak solution. We give extensive numerical evidence that the scheme does converge to the entropy solution, and that the order of convergence away from singularities is optimal; i.e., equal to 2 in the norm of L infinity (L(loc)infinity).
引用
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页码:337 / 361
页数:25
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