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有限元第三版,理论、快速求解器和在固体力学中的应用
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作者 dietrich braess 吴永礼 《国外科技新书评介》 2008年第4期14-15,共2页
本书是根据作者在德国鲁尔大学的讲课内容编写而成,原文为德文。 有限元法已经成为椭圆型和抛物型偏微分方程数值解的主要工具之一,它基于微分方程的变分公式,比有限差分法和有限体积法更灵活,因此,可用于复杂的问题,以往,有限... 本书是根据作者在德国鲁尔大学的讲课内容编写而成,原文为德文。 有限元法已经成为椭圆型和抛物型偏微分方程数值解的主要工具之一,它基于微分方程的变分公式,比有限差分法和有限体积法更灵活,因此,可用于复杂的问题,以往,有限元法由数学家和工程师分别进行研究,本书则将这两方面的结果系统地结合在一起。 展开更多
关键词 有限元法 固体力学 偏微分方程数值解 求解器 有限体积法 有限差分法
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ERROR REDUCTION IN ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC OBSTACLE PROBLEMS
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作者 dietrich braess Carsten Carstensen Ronald H.W.Hoppe 《Journal of Computational Mathematics》 SCIE CSCD 2009年第2期148-169,共22页
We consider an adaptive finite element method (AFEM) for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error wh... We consider an adaptive finite element method (AFEM) for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error which leads to R-linear convergence. This result is shown to hold up to a consistency error due to the extension of the discrete multipliers (point functionals) to H^-1 and a possible mismatch between the continuous and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type error estimator consisting of element and edge residuals. The a posteriori error analysis reveals that the significant difference to the unconstrained case lies in the fact that these residuals only have to be taken into account within the discrete noncoincidence set. The proof of the error reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM. 展开更多
关键词 Adaptive finite element methods Elliptic obstacle problems Convergence analysis
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