Elliptic Variational Inequalities and Their Numerical Approximations

Variational inequalities form an important family of nonlinear problems. Some of the more complex physical processes are described by variational inequalities. Several comprehensive monographs can be consulted for the theory and numerical solution of variational inequalities, e.g., [59], [70], [76], [78], [121], [122], [159]. We study standard elliptic variational inequalities (EVIs) in this chapter. We give a brief introduction to some well-known results on the existence, uniqueness and stability of solutions to elliptic variational inequalities. We also discuss numerical approximations of EVIs and their error analysis.