Numerical Treatment of Partial Differential EquationsSpringer Science & Business Media, 04.10.2007 - 596 Seiten Many well-known models in the natural sciences and engineering, and today even in economics, depend on partial di?erential equations. Thus the e?cient numerical solution of such equations plays an ever-increasing role in state-- the-art technology. This demand and the computational power available from current computer hardware have together stimulated the rapid development of numerical methods for partial di?erential equations—a development that encompasses convergence analyses and implementational aspects of software packages. In 1988 we started work on the ?rst German edition of our book, which appeared in 1992. Our aim was to give students a textbook that contained the basic concepts and ideas behind most numerical methods for partial di?er- tial equations. The success of this ?rst edition and the second edition in 1994 encouraged us, ten years later, to write an almost completely new version, taking into account comments from colleagues and students and drawing on the enormous progress made in the numerical analysis of partial di?erential equations in recent times. The present English version slightly improves the third German edition of 2005: we have corrected some minor errors and added additional material and references. |
Inhalt
Weak Solutions | 125 |
The Finite Element Method | 173 |
Finite Element Methods for Unsteady Problems | 317 |
Singularly Perturbed Boundary Value Problems 375 | 376 |
Variational Inequalities Optimal Control | 436 |
Numerical Methods for Discretized Problems | 499 |
571 | |
585 | |
Andere Ausgaben - Alle anzeigen
Numerical Treatment of Partial Differential Equations Christian Grossmann,Hans-Görg Roos,Martin Stynes Eingeschränkte Leseprobe - 2007 |
Häufige Begriffe und Wortgruppen
analysis ansatz ansatz functions applied approximation arbitrary Assume basis functions bilinear form boundary conditions boundary value problem bounded choose coefficients computed consider continuous convergence convex decomposition defined definition denote derivatives differential operator discrete problem discrete space domain eigenvalues equivalent error estimates example exists a constant finite difference methods finite element finite element method finite volume method first Galerkin method given grid points Hence implies initial-boundary value problem integrals interpolation iteration L2 norm Lagrange Lax-Milgram lemma layer linear system M-matrix maximum norm mesh points numerical obtain optimal parameter penalty method piecewise linear polynomials Proof prove quadrature Remark satisfies scalar product scheme second-order semi-discretization smooth Sobolev spaces solve spatial stability stiffness matrix subdomains technique Theorem triangle uk+1 unique solution V-elliptic variational equation variational inequality variational problem vector weak formulation yields