A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam (). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
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A Posteriori Error Analysis Via Duality Theory: With Applications in ...
Limited preview - 2004
adapted mesh assumption auxiliary function Banach space bilinear form boundary condition boundary value problem conjugate functions consider constant constraint set convergence convex convex functions corner domain defined denote derive a posteriori Dirichlet domain Q dual problem duality theory ED(u energy function error bound f in Q finite element method finite element solution freedom Figure g on 69 g1 on T1 Gâteaux derivative Gâteaux differentiable gradient recovery type idealized Kačanov iterates Kačanov method Lax-Milgram Lemma Lemma Let Q linear problem linearized elasticity Lipschitz continuous Lipschitz domain mathematical minimization problem model problem nodes nonlinear nonlinear problem Number of degrees numerical results obstacle problem obtain parameter posteriori error analysis posteriori error estimates sequence side Sobolev spaces solution u0 solving subsection torsion problem triangle uniform mesh unique solution upper bound v e H'(Q variational inequality weak formulation