By Weimin Han
This quantity offers a posteriori blunders research for mathematical idealizations in modeling boundary worth difficulties, specifically these coming up in mechanical functions, and for numerical approximations of various nonlinear variational difficulties. the writer avoids giving the implications within the such a lot normal, summary shape in order that it really is more straightforward for the reader to appreciate extra basically the fundamental rules concerned. Many examples are integrated to teach the usefulness of the derived errors estimates.
This quantity is acceptable for researchers and graduate scholars in utilized and computational arithmetic, and in engineering.
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Additional info for A Posteriori Error Analysis via Duality Theory: With Applications in Modeling and Numerical Approximations
Chapter 2 ELEMENTS OF CONVEX ANALYSIS, DUALITY THEORY The a posteriori error estimates presented in this work are derived based on the duality theory of convex analysis. The first research monograph specifically devoted to the topic of convex analysis is , emphasizing the finitedimensional case. Convex analysis and duality theory in general normed spaces, mostly infinite dimensional ones, are thoroughly discussed in the well-known reference . Another comprehensive treatment of the topic is .
26 ( A N OBSTACLE PROBLEM) A representative example of the elliptic variational inequality of the first kind is given by the obstacle problem. The problem is to determine the equilibrium position of an elastic membrane passing through the boundary of a planar domain, lying above an obstacle of height $, and being subject to the action of a vertical force of density T f , here 7 is the elastic tension of the membrane, and f is a given function. Denote by R the planar domain, and by r for its boundary.
38 A POSTERIORI ERROR ANALYSIS VIA DUALITY THEORY in V. 29, Ui>lVN, stands for the closure of Ui>lVN, inequality also serves a s a basis for error estimates. When the finite dimensional space VN is constructed from piecewise (images of) polynomials, the Galerkin method leads to a finite element method. In other words, the finite element method (FEM) is a Galerkin method with the use of piecewise (images of) polynomials over a finite element partition of the domain 0. The finite element method today is the dominant numerical method for solving problems in structural mechanics and is popularly used in fluid mechanics.
A Posteriori Error Analysis via Duality Theory: With Applications in Modeling and Numerical Approximations by Weimin Han