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Summation By Parts Finite Difference Methods with Simultaneous Approximation Terms for the Heat Equation with Discontinuous Coefficients
Linnaeus University, Faculty of Technology, Department of Mathematics.
2019 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one.

Place, publisher, year, edition, pages
2019. , p. 39
Keywords [en]
Finite Difference Method, FDM, Summation By Parts, Simultaneous Approximation Terms, SBP-SAT, Heat Equation, Poisson's Equation, Discontinuous Coefficients, Piecewise Constant Coefficients, Convergence, Dual Consistency, Stability
National Category
Computational Mathematics Discrete Mathematics Mathematical Analysis Other Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-84777OAI: oai:DiVA.org:lnu-84777DiVA, id: diva2:1321660
Subject / course
Numerical Analysis
Educational program
Applied Mahtematics Programme, 180 credits
Supervisors
Examiners
Available from: 2019-06-11 Created: 2019-06-09 Last updated: 2019-06-12Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
  • html
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  • asciidoc
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