Характер сходимости схем при расчете на адаптивных сетках задач со слоями

Translated title of the contribution: Convergence behavior of popular schemes in case of calculating on adaptive grids problems with layers

Research output: Contribution to journalArticlepeer-review

Abstract

The paper compares solution quality to some model second-order equation with a small parameter obtained through three different schemes both on special adaptive grids specified explicitly by coordinate transformations eliminating layers and on uniform grids in a new coordinate related to the transformations. The schemes up to second order in physical and transformation variables both with a diagonal and not diagonal dominance and the simplest counter-flow scheme are analyzed. Predictions of a solution behavior based on estimates of solution errors are described, which are confirmed by numerical experiments and proofs. It is established, in particular, that the scheme of the second order with a diagonal dominance converges uniformly if the coefficient before the second derivative is small at the points of the boundary layer only. It was also demonstrated for the schemes without a diagonal dominance, mach better solutions without oscillations are obtained on uniform grids in new variables than on corresponding adaptive grids in the original physical coordinates.

Translated title of the contributionConvergence behavior of popular schemes in case of calculating on adaptive grids problems with layers
Original languageRussian
Article number5
Pages (from-to)66-79
Number of pages14
JournalJournal of Computational Technologies
Volume25
Issue number5
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Adaptive grid
  • Boundary layer
  • Diagonal dominance
  • Small parameter
  • Uniform convergence

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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