A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Google eBook)
This volume 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 variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.
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Theoretical Numerical Analysis: A Functional Analysis Framework
Kendall E. Atkinson,Weimin Han
Limited preview - 2001
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adapted mesh applying Theorem 2.40 assumption auxiliary function boundary condition boundary value problem comer conjugate functions consider constraint set convergence convex convex functions deﬁned deﬁnition denote derive a posteriori differential equation Dirichlet dual problem duality theory efﬁciency eigenvalue elliptic variational inequality energy function error bound f in Q ﬁnd Finite Element Method ﬁnite element solution ﬁrst ﬂow Gateaux derivative gradient recovery type Hence idealization Kacanov iteration Kacanov method Lax-Milgram Lemma Lemma linear problem linearized elasticity Lipschitz continuous Lipschitz domain Math mathematical minimization problem model problem nodes nonlinear problem Numerical Analysis numerical results obstacle problem obtain oo otherwise parameter posteriori error analysis posteriori error estimates Q F2 quantity regularization method satisﬁes sequence side Sobolev spaces solving subsection tensor torsion problem triangle uniform mesh unique solution upper bound variational inequality weak formulation