An approach to adaptive grid construction for non-stationary problems

Dar'in, N. A.; Mazhukin, V. I.

doi:10.1016/0041-5553(88)90150-4

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1999

2018

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“…This method is proved to be effective for solution of wide range of problems of mathematical physics such as nonlinear heat conductivity,11,12 nonlinear transfer (Burger's equation), gas dynamics,13 one-and multidimensional Stephan problems. 16,17 Differential problems written in different coordinate systems are equivalent from the mathematical point of view. It is intrinsic to demand a realization of similar property for difference schemes.…”

Section: Introductionmentioning

confidence: 99%

Invariant Difference Schemes for Parabolic Equations With Transformations of Independent Variables

Samarskiî

Mazhukin

Матус

et al. 1999

Math. Models Methods Appl. Sci.

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In this paper, invariant difference schemes for nonstationary equations under independent variables transformation constructed and investigated. Under invariance of difference scheme we mean its ability to preserve basic properties (stability, approximation, convergency, etc.) in various coordinate systems. Difference schemes of the second-order approximation that satisfy the invariance property are constructed for equations of parabolic type. Stability and convergency investigation of correspondent difference problems are carried out; a priori estimates in various grid norms are obtained.

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Section: Introductionmentioning

confidence: 99%