Adaptive Linienmethoden für nichtlineare parabolische Systeme in einer Raumdimension

Abstract: "A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi-implicit Euler discre...

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Bibliographische Detailangaben
1. Verfasser: Nowak, Ulrich (VerfasserIn)
Format: UnknownFormat
Sprache:eng
Veröffentlicht: Berlin Konrad-Zuse-Zentrum für Informationstechnik Berlin 1993
Schriftenreihe:Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Technical report 1993,14
Schlagworte:
Differential equations, Parabolic > Nichtlineares System > Mehrgitterverfahren > Nichtlineare Differentialgleichung > Linienmethode > Adaptives Gitter > Parabolische Differentialgleichung > Hochschulschrift
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Zusammenfassung:Abstract: "A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi-implicit Euler discretization. Space discretization is done with finite differences on non-uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously
Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way.
Beschreibung:Zugl.: Berlin, Freie Univ., Diss., 1993
Beschreibung:III, 177 S.
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