一类非线性双曲型方程有限元方法的误差分析

关于二阶双曲型方程有限元方法的理论研究,已有不少工作,如1]—5]。5]对具Dirichlet边界条件且初边值均取0值的一类非线性双曲方程定解问题的有限元方法,导出了H~1-逼近阶估计,其中,对有关辅助函数u(5],p,151)施加了||?u||_(L~∞(Ω×0,T]))< ∞的假定。 本文对5]中研究过的方程,就Dirichlet边界及第三类边界两种情况,给出了半离散Galerkin方法H~1及L~2误差估计。得到的逼近阶都是最佳的,而且,在建立H~1估计的

ERROR ANALYSIS OF THE FEM FOR A CLASS OF NONLINEAR HYPERBOLIC EQUATION

Yuan Yi-rang has derived the H~1 error estimate of the finite element method fora class of nonlinear hyperbolic equation with Dirichlet boundary condition and zeroinitial boundary value. For that equation with Dirichlet boundary condition or the thirdboundary condition, this paper gives H~1 and L~2 error estimates of the semi-discrete Ga-lerkin method, and the approximation orders obtained are optimal.