On Galerkin Methods

Wendland W.L.

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On Galerkin Methods

机译：关于Galerkin方法

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The classical Ritz-Galerkin method for variational problems is stable and convergent if, for linear problems, the underlying functional is coercive. For pseudo-diferential equations, the more general essential property is strong ellipticity. For Galerkin-Petrov methods, an additional mapping of the test onto the trial spaces allows the reduction of the stability and convergence analysis from rather general problems and methods to the above mentioned standard case. Several examples of this approach will be presented including collocation methods for elliptic boundary integral equations and also Galerkin-like schemes for nonelliptic problems.

机译：如果对于线性问题，基础函数是强制性的，则经典的Ritz-Galerkin方法对于变分问题是稳定且收敛的。对于伪微分方程，更一般的基本性质是强椭圆率。对于Galerkin-Petrov方法，将测试映射到试验空间可以使稳定性和收敛性分析从相当普遍的问题和方法减少到上述标准案例。将介绍此方法的几个示例，包括用于椭圆边界积分方程的搭配方法，以及用于非椭圆问题的类似Galerkin方案。

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |1996年第s2期|p.257-260|共4页
作者
Wendland W.L.;
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正文语种 eng
中图分类应用数学;
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On Galerkin Methods

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