Galerkin alternating-direction method for a kind of three-dimensional nonlinear hyperbolic problems

Authors:
Xiang Lai;Yirang Yuan
Affiliations:
Department of Mathematics, Shandong University, Jinan 250100, Shandong, China;Department of Mathematics, Shandong University, Jinan 250100, Shandong, China
Venue:
Computers & Mathematics with Applications
Year:
2009

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An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables

SIAM Journal on Numerical Analysis

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Abstract

A kind of three-dimensional nonlinear hyperbolic equation is firstly transformed into a first-order system of equations, then the Galerkin alternating-direction procedure for the system is derived. The error estimates of the procedure in H^1 norm and L^2 norm, respectively, are obtained by using the theory and techniques of priori estimate of differential equations. The numerical experiment is also given to support the theoretical analysis. Comparing the results of numerical example with the theoretical analysis, they are coincided.