Nonlinear Elliptic and Evolution Problems and Their Finite Element Aproximations

The main objectives of this book are both the theoretical and computational presentation of the finite element method for linear and nonlinear elliptic and evolution problems. An important aspect of the theoretical treatment lies in the proofs of the convergence of approximate solutions to the exact ones and in the error estimates given for various regularity assumptions. Relevant computational details are discussed with reference to a number of computer programs. Particularly noteworthy is the coverage given to novel developments in the treatment of evolutionary problems.****Although this volume contains a number of sophisticated recent advances, its clear and straightforward exposition makes it valuable for researchers and engineers as well as newcomers to the finite element method.

Provides a survey of the theory of function spaces as used in finite element methods**Covers new approaches to the proofs of convergence and optimum error estimates**Algorithms and numerical aspects are represented for both linear and nonlinear problems