J 2013

Analysis and application of the discontinuous Galerkin method to the RLW equation

HOZMAN, Jiří and Jan LAMAČ

Basic information

Original name

Analysis and application of the discontinuous Galerkin method to the RLW equation

Authors

HOZMAN, Jiří (203 Czech Republic, belonging to the institution) and Jan LAMAČ (203 Czech Republic)

Edition

BOUNDARY VALUE PROBLEMS, 2013, 1687-2770

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

General mathematics

Country of publisher

Switzerland

Confidentiality degree

is not subject to a state or trade secret

References:

RIV identification code

RIV/46747885:24510/13:#0001000

Organization

Faculty of Science, Humanities and Education – Technical University of Liberec – Repository

UT WoS

000320662500001

Keywords in English

experimental order of convergence

Links

EE2.3.09.0155, research and development project.
Changed: 30/3/2015 09:57, Jiří Hozman

Abstract

V originále

In this work, our main purpose is to develop of a sufficiently robust, accurate and efficient numerical scheme for the solution of the regularized long wave (RLW) equation, an important partial differential equation with quadratic nonlinearity, describing a large number of physical phenomena. The crucial idea is based on the discretization of the RLW equation with the aid of a combination of the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. Furthermore, a suitable linearization preserves a linear algebraic problem at each time level. We present error analysis of the proposed scheme for the case of nonsymmetric discretization of the dispersive term. The appended numerical experiments confirm theoretical results and investigate the conservative properties of the RLW equation related to mass, momentum and energy. Both procedures illustrate the potency of the scheme consequently.