Finite difference schemes with transferable interfaces for parabolic problems

Sofia Eriksson; Jan Nordström

doi:10.1016/j.jcp.2018.08.051

Finite difference schemes with transferable interfaces for parabolic problems

Sofia Eriksson, Jan Nordström

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent.

Original language	English
Pages (from-to)	935-949
Number of pages	15
Journal	Journal of Computational Physics
Volume	375
DOIs	https://doi.org/10.1016/j.jcp.2018.08.051
Publication status	Published - 15 Dec 2018
Externally published	Yes

Keywords

Dual consistency
Finite difference methods
High order accuracy
Interfaces
Summation-by-parts
Superconvergence

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2018.08.051

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title = "Finite difference schemes with transferable interfaces for parabolic problems",

abstract = "We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent.",

keywords = "Dual consistency, Finite difference methods, High order accuracy, Interfaces, Summation-by-parts, Superconvergence",

author = "Sofia Eriksson and Jan Nordstr{\"o}m",

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AU - Eriksson, Sofia

AU - Nordström, Jan

PY - 2018/12/15

Y1 - 2018/12/15

N2 - We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent.

AB - We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent.

KW - Dual consistency

KW - Finite difference methods

KW - High order accuracy

KW - Interfaces

KW - Summation-by-parts

KW - Superconvergence

UR - http://www.scopus.com/inward/record.url?scp=85053206186&partnerID=8YFLogxK

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M3 - Article

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SN - 0021-9991

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SP - 935

EP - 949

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Finite difference schemes with transferable interfaces for parabolic problems

Abstract

Keywords

ASJC Scopus subject areas

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