On error estimates in the Galerkin method for hyperbolic equations

S. E. Zhelezovski

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On error estimates in the Galerkin method for hyperbolic equations

机译：关于双曲型方程的Galerkin方法中的误差估计

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We consider the Cauchy problem in a Hilbert space for a second-order abstract quasilinear hyperbolic equation with variable operator coefficients and nonsmooth (but Bochner integrable) free term. For this problem, we establish an a priori energy error estimate for the semidiscrete Galerkin method with an arbitrary choice of projection subspaces. Also, we establish some results on existence and uniqueness of an exact weak solution. We give an explicit error estimate for the finite element method and the Galerkin method in Mikhlin form.

机译：我们考虑具有可变算子系数和非光滑（但Bochner可积）自由项的二阶抽象拟线性双曲方程在希尔伯特空间中的柯西问题。针对此问题，我们为半离散Galerkin方法建立了先验能量误差估计，并可以任意选择投影子空间。同样，我们建立了关于精确弱解的存在性和唯一性的一些结果。我们以Mikhlin形式给出了有限元方法和Galerkin方法的显式误差估计。

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《Siberian Mathematical Journal》 |2005年第2期|共12页
作者
S. E. Zhelezovski;
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正文语种 eng
中图分类数学;
关键词
second-order hyperbolic equation; the Galerkin method; error estimate; weak solution; existence and uniqueness of a solution; finite element method;

机译：二阶双曲方程;Galerkin方法;误差估计;弱解;解的存在唯一性;有限元法;

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On error estimates in the Galerkin method for hyperbolic equations

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