A Local Discontinuous Petrov-Galerkin Method for Partial Differential Equations with High Order Derivatives

doi:10.19596/j.cnki.1001-246x.7919

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2019, Vol. 36 ›› Issue (5): 517-532.DOI: 10.19596/j.cnki.1001-246x.7919

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A Local Discontinuous Petrov-Galerkin Method for Partial Differential Equations with High Order Derivatives

ZHAO Guozhong¹, YU Xijun², GUO Hongping¹, DONG Ziming¹

1. Faculty of Mathematics, Baotou Teachers'College, Baotou 014030, China;
2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2018-07-04 Revised:2018-09-22 Online:2019-09-25 Published:2019-09-25
Supported by:
National Natural Science Foundation of China (11761054, 11571002, 11261035), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-15-A07), Natural Science Foundation of Inner Mongolia Autonomous Region, China (2015MS0108, 2012MS0102) and Science Research Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region, China (NJZZ12198, NJZZ16234, NJZZ16235)

Abstract

Abstract: A local discontinuous Petrov-Galerkin method is proposed for solving three types of partial differential equations with second, third and fourth order derivatives, respectively. They are Burgers type equations, KdV type equations and bi-harmonic type equations. The method extends discontinuous Petrov-Galerkin method for conservation laws by rewriting corresponding equations into a first order system and solving the system instead of the original equation. The method has a fourth order accuracy and maintains advantages of discontinuous Petrov-Galerkin method. Numerical simulations verify that the method reaches optimal convergence order and simulates well complex wave interaction such as soliton propagation and collision.

Key words: KdV type equation, bi-harmonic equation, local discontinuous Petrov-Galerkin method, soliton evolution

CLC Number:

O241.82

ZHAO Guozhong, YU Xijun, GUO Hongping, DONG Ziming. A Local Discontinuous Petrov-Galerkin Method for Partial Differential Equations with High Order Derivatives[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(5): 517-532.

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A Local Discontinuous Petrov-Galerkin Method for Partial Differential Equations with High Order Derivatives

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