Fujita H., Saito N., Suzuki T. Operator theory and numerical methods

Amsterdam: Elsevier. – 2001. – 318 p. Recent developments in numerical computations are amazing. A lot of huge projects in applied and theoretical sciences are becoming successful by them, while similar things are happening even in the level of personal computers. Under such a situation, theoretical studies on numerical schemes are fruitful and highly needed. The purpose of the present book is to provide some of them, particularly for schemes to solve partial differential equations. In 1991, we published an article on the finite element method applied to evolutionary problems from Elsevier Publishers. This book follows basically that way of description. We study various schemes from the operator theoretical point of view. Many parts are devoted to the finite element method. We deal with elliptic and then time dependent problems in use of the semigroup theory and so forth. Some other schemes and problems are also discussed, with the later development taken also into account. We are led to believe that any scheme used practically has significant and tight structures mathematically and the converse is also true.Elliptic Boundary Value Problems and FEM.
Semigroup Theory and FEM.
Evolution Equations and FEM.
Other Methods in Time Discretization.
Other Methods in Space Discretization.
Nonlinear Problems.
Domain Decomposition Method.