Analysis

Download A posteriori error analysis via duality theory : with by Weimin Han PDF

By Weimin Han

ISBN-10: 0387235361

ISBN-13: 9780387235363

This paintings offers a posteriori blunders research for mathematical idealizations in modeling boundary worth difficulties, in particular these coming up in mechanical purposes, and for numerical approximations of diverse nonlinear var- tional difficulties. An mistakes estimate is named a posteriori if the computed resolution is utilized in assessing its accuracy. A posteriori errors estimation is vital to m- suring, controlling and minimizing blunders in modeling and numerical appr- imations. during this publication, the most mathematical instrument for the advancements of a posteriori errors estimates is the duality idea of convex research, documented within the recognized booklet through Ekeland and Temam ([49]). The duality idea has been stumbled on beneficial in mathematical programming, mechanics, numerical research, and so on. The publication is split into six chapters. the 1st bankruptcy studies a few simple notions and effects from sensible research, boundary worth difficulties, elliptic variational inequalities, and finite aspect approximations. the main proper a part of the duality thought and convex research is in short reviewed in bankruptcy 2.

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Example text

SINGULARITIES OF ELLIPTIC PROBLEMS ON PLANAR NONSMOOTH DOMAINS The most significant property of elliptic boundary value problems on a smooth domain is the so-called "shift theorem". Roughly speaking, "shift theorem" states: For an elliptic boundary value problem on a smooth domain, the smoother the data (the coefficients, the right-hand side and the boundary value), the smoother the solution. As an example, consider the boundary value problem Assume d R is smooth. Then for any integer k 2 0, f E H k ( R ) implies uE H~+~(R).

The interested reader is referred to [107]. More recent comprehensive references on the topic are [99, 1001. In the literature, one may find many other results on the topic. , theoretical and computational aspects of singularities for elasticity systems are studied. The papers [92] and [I231 are devoted to a study of regularity of solutions of Stokes problems in a polygon. For boundary value problems of the biharmonic equation on comer domains, see [23], etc. For both edge and corner singularities in a three dimensional polyhedron, cf.

Consider the subdifferential of the indicator function 0 +cc i f v ~ K , i f v $! K. If u $! K , then d I K ( u )= 0. Assume u E K.

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