Weimin Han's A Posteriori Error Analysis Via Duality Theory: With PDF

By Weimin Han

ISBN-10: 0387235361

ISBN-13: 9780387235363

ISBN-10: 038723537X

ISBN-13: 9780387235370

This quantity offers a posteriori blunders research for mathematical idealizations in modeling boundary worth difficulties, particularly these coming up in mechanical purposes, 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 straightforward for the reader to appreciate extra truly the basic rules concerned. Many examples are incorporated to teach the usefulness of the derived errors estimates.

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

Example text

U,. DEFINITION 2 . , f ( u )and f ( v )are not simultaneously infinite with opposite signs. 3 Let K be a convex set in V avtd f : K f ( v )= +R. If { y; w v E K, v is convex, then we say f is convex on K. 1) holds for any u, v E K , u # v and t E ( 0 , l ) . 3. In other words, we will use the same symbol f for both the function defined on K and its extension by oo to the complement of K in the space V. Thus, we will say that a function is convex over a subset K c V to mean that the extension of the function is convex in the space V.

We denote by C : R x Sd -+ S d the elasticity tensor of the material. We assume the fourth-order elasticity tensor C to be symmetric: and pointwise stable: for some constant co > 0, We first describe the physical setting of the frictional contact problem. Details and other related problems can be found in [94, 811. The boundary F is parelastic body occupying the domain R inIRd, dtitioned into possibly three parts: F = rDU F N U rc with r D , rNand relatively open and mutually disjoint, and meas(FD) > 0.

Mathematical theory of these methods can be found in [33,135]. g. [63]. Theory of the finite element method for solving parabolic problems can be found in [I471 and more recently in [148]. Finally, we list a few representative engineering books on the finite element method, [20, 88, 163, 1641. The reader is referred to two historical notes [115, 1621 on the development of the finite element method. In this section, we will review some results of the finite element method. There are some basic aspects in the construction of finite element approximations.

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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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