Download e-book for iPad: A Posteriori Error Analysis via Duality Theory: With by Weimin Han

By Weimin Han

ISBN-10: 0387235361

ISBN-13: 9780387235363

This quantity presents a posteriori errors research for mathematical idealizations in modeling boundary price difficulties, in particular these coming up in mechanical functions, and for numerical approximations of various nonlinear variational difficulties. the writer avoids giving the consequences within the such a lot common, summary shape in order that it's more uncomplicated for the reader to appreciate extra sincerely the fundamental principles concerned. Many examples are incorporated to teach the usefulness of the derived blunders estimates.

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This quantity is acceptable for researchers and graduate scholars in utilized and computational arithmetic, and in engineering.

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Extra resources for A Posteriori Error Analysis via Duality Theory: With Applications in Modeling and Numerical Approximations

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Assume a : V x V + JR is a continuous, V-elliptic bilinear form and e : V -+ R is a linear continuous functional. 25 Let V be a Hilbert space. c. on V and e : V -+ IR is a linear continuousfunctional. 28). Therefore, elliptic variational inequalities of the first kind can be viewed as special cases of elliptic variational inequalities of the second kind. 29) where j is a real valued functional. In this connection, one can also study the following mixed type variational inequality where the set K, the bilinear form a ( .

0 Each K is a triangle or quadrilateral with a nonempty interior K . For distinct K 1 ,K z E Ph, K 1 f l K 2 is either empty, or a common vertex, a common side or a common face of K l and K 2 . For any K E Ph, its diameter diam ( K ) 5 h. The assumption that the domain R is a polygon ensures that it can be partitioned into straight-sided triangles and quadrilaterals. 7 for a finite element mesh. For convenience in practical implementation as well as in theoretical analysis, it is assumed that there exist a finite number of fixed polyhedra, called reference elements or master elements, ambiguously represented by one symbol K ,such that for each element K , there is an invertible affine mapping function FK with K = FK ( K ).

For a vector v , we will use its normal component v, = v v and tangential component v, = v - v,v at a point on the boundary. Similarly for a tensor a E Sd, we define its normal component a, = a v . v and tangential component a, = a v - a,v. For a detailed treatment of traces for vector and tensor fields in contact problems and related spaces see [94] or [81]. ~ t = ~ 33 Preliminaries The material we consider here is linearly elastic. We denote by C : R x Sd -+ S d the elasticity tensor of the material.

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A Posteriori Error Analysis via Duality Theory: With Applications in Modeling and Numerical Approximations by Weimin Han


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