首页> 外文期刊>Jahresbericht der Deutschen Mathematiker-Vereinigung >Klaus Boennier: 'Numerical Methods for Nonlinear Elliptic Differential Equations-A Synopsis' Oxford University Press, 2010,776 pp.
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Klaus Boennier: 'Numerical Methods for Nonlinear Elliptic Differential Equations-A Synopsis' Oxford University Press, 2010,776 pp.

机译:Klaus Boennier:“非线性椭圆型微分方程的数值方法-提要”,牛津大学出版社,2010年,776页。

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摘要

The book is mainly concerned with numerical analysis and convergence theory of various methods for numerically solving boundary value problems with nonlinear elliptic partial differential equations. Particular emphasis is put on a general theoretical discretization framework, which allows the formulation of most of the numerical methods studied here as special cases. This general concept essentially consists of an abstract Petrov-Galerkin method, formulated with suitable projection operators mapping the continuous spaces involved onto their discrete counterparts. For many important discretization methods, convergence is studied in the book on the basis of this general framework, using the classical way via consistency and stability.
机译:该书主要涉及用非线性椭圆型偏微分方程数值求解边值问题的各种方法的数值分析和收敛理论。特别强调的是一般的理论离散化框架,该框架允许将此处研究的大多数数值方法表述为特殊情况。这个基本概念基本上由抽象的Petrov-Galerkin方法组成,该方法由适当的投影算符构成,将涉及的连续空间映射到离散的对应对象上。对于许多重要的离散化方法,本书在此通用框架的基础上使用经典的方式通过一致性和稳定性来研究收敛性。

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