Arbitrary dimension convection–diffusion schemes for space–time discretizations

Randolph E. Bank, Panayot S. Vassilevski, Ludmil Tomov Zikatanov

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

This note proposes embedding a time dependent PDE into a convection–diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space–time domain demonstrate the feasibility of the proposed approach.

Original languageEnglish (US)
Pages (from-to)19-31
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume310
DOIs
StatePublished - Jan 15 2017

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Convection-diffusion
Convergence of numerical methods
Error analysis
Discretization
Space-time
Streamline Diffusion
Finite Element
Discretization Scheme
Arbitrary
Error Analysis
Higher Dimensions
Stability Analysis
Singularity
Numerical Results
Demonstrate

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Arbitrary dimension convection–diffusion schemes for space–time discretizations. / Bank, Randolph E.; Vassilevski, Panayot S.; Zikatanov, Ludmil Tomov.

In: Journal of Computational and Applied Mathematics, Vol. 310, 15.01.2017, p. 19-31.

Research output: Contribution to journalArticle

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AU - Zikatanov, Ludmil Tomov

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AB - This note proposes embedding a time dependent PDE into a convection–diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space–time domain demonstrate the feasibility of the proposed approach.

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