## Download PDF by Weimin Han: A Posteriori Error Analysis Via Duality Theory: With

By Weimin Han

ISBN-10: 0387235361

ISBN-13: 9780387235363

ISBN-10: 038723537X

ISBN-13: 9780387235370

This quantity presents a posteriori errors research for mathematical idealizations in modeling boundary worth difficulties, in particular these coming up in mechanical purposes, and for numerical approximations of diverse nonlinear variational difficulties. the writer avoids giving the consequences within the such a lot normal, summary shape in order that it really is more uncomplicated for the reader to appreciate extra in actual fact the basic rules concerned. Many examples are integrated to teach the usefulness of the derived errors estimates.

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**Additional info for A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Advances in Mechanics and Mathematics)**

**Example text**

N O . 54) Recall that { & ) z , are the basis functions of the space x associated with the nodal points { h i ) F l with the property that We define #f=&oFil, i=1,. . , No. Then the functions { @ ) Z 1 have the property that Hence, {@)zl form a set of basis functions for the space X K Finite element spaces. A global finite element function vh is defined piecewise by the formula v h l ~E X K V K E Ph. A natural question is whether such finite element functions can be directly used to solve a boundary value problem.

35) is the equilibrium equation. With a = (aij)dXd, D i v a : R + Ktd is defined by A POSTERIORI ERROR ANALYSIS VIA DUALITY THEORY 34 where the summation convention is used. 37). 41). 38). 41) represent Tresca's friction law. In certain situations, the frictional contact problem stated above describes the material deformation quite accurately. In more complicated situations, such as when the contact zone is not prescribed a priori or when more realistic frictional contact laws are used, the frictional contact problem here can be viewed as an intermediate problem for a typical step in an iterative solution procedure for solving the more complicated contact problem.

The smaller h is, the finer the mesh. We say a family of triangulations { P h ) h is regular if 1 there exists a constant a 2 1 such that 2 the discretization parameter h + 0. e, the minimal angles of all the elements are bounded below away from 0. Polynomial spaces on the reference elements. Function spaces over a general element can be constructed from those on the reference element. Thus we first introduce a polynomial space x on K. Although it is possible to choose other finite dimensional function spaces as X, the overwhelming choice of x for practical use is a polynomial space, due to the simplicity in constructing a polynomial and the good approximation property of polynomial spaces.

### A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Advances in Mechanics and Mathematics) by Weimin Han

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