Preliminaries -- Elements of Convex Analysis, Duality Theory -- A Posteriori Error Analysis for Idealizations in Linear Problems -- A Posteriori Error Analysis for Linearizations -- A Posteriori Error Analysis for Some Numerical Procedures -- Error Analysis for Variational Inequalities of the Second Kind.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. Audience This volume is suitable for researchers and graduate students in applied and computational mathematics, and in engineering.