The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case

Author:

Cockburn Bernardo,Hou Suchung,Shu Chi-Wang

Abstract

In this paper we study the two-dimensional version of the Runge-Kutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-ordrr accurate. Preliminary numerical results showing the performance of the schemes on a variety of initial-boundary value problems are shown.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference43 articles.

1. First order quasilinear equations with boundary conditions;Bardos, C.;Comm. Partial Differential Equations,1979

2. J. B. Bell, C. N. Dawson, and G. R. Shubin, An unsplit, higher-order Godunov method for scalar conservation laws in multiple dimensions, J. Comput. Phys. 74 (1988), 1-24.

3. G. Chavent, B. Cockburn, G. Cohen, and J. Jaffré, A discontinuous finite element method for nonlinear hyperbolic equations, Innovative Numerical Methods in Engineering (Proc. 4th Internat. Sympos. (Georgia Institute of Technology, Atlanta, Georgia), Springer-Verlag, 1986, pp. 337-342.

4. Studies in Mathematics and its Applications, Vol. 4;Ciarlet, Philippe G.,1978

5. B. Cockburn and C.-W. Shu, The Runge—Kutta local projection 𝑃¹ discontinuous Galerkin finite element method for scalar conservation laws, Institute for Mathematics and its Applications Preprint Series # 388, Univ. of Minnesota (1988); Proceedings of First National Fluid Dynamics Congress, Cincinnati, Ohio, July 24-28, 1988; to appear in 𝑀²𝐴𝑁.

Cited by 28 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3