The goal of this book is to highlight some central areas in current research on the numerical solution of elliptic problems. Mathematical models involving elliptic partial differential equations arise in a variety of real-life problems in science and engineering. Besides phenomena fully described by an elliptic equation, also time-dependent problems describing various evolutionary processes often lead to elliptic problems as subproblems arising in the course of the solution procedure. Furthermore, saddle-point problems of Stokes type, which are not elliptic in a strict sense, can be considered elliptic in a wider sense, being stationary problems that can be reduced to coercivity via the Schur complement operator. These facts reinforce the fundamental role of elliptic problems and their efficient numerical solution.
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