Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative

Hannes Frenander; Jan Nordström

doi:10.1002/num.22210

Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative

Hannes Frenander, Jan Nordström

Linköping University

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

2 Citations (Scopus)

Abstract

A one-dimensional steady-state advection-diffusion problem using summation-by-parts operators is investigated. For approximating the second derivative, a wide stencil is used, which simplifies implementation and stability proofs. However, it also introduces spurious, oscillating, modes for all mesh sizes. We prove that the size of the spurious modes are equal to the size of the truncation error for a stable approximation and hence disappears with the convergence rate. The theoretical results are verified with numerical experiments.

Original language	English
Pages (from-to)	501-517
Number of pages	17
Journal	Numerical Methods for Partial Differential Equations
Volume	34
Issue number	2
DOIs	https://doi.org/10.1002/num.22210
Publication status	Published - Mar 2018
Externally published	Yes

Keywords

oscillating solutions
spurious solutions
summation-by-parts

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1002/num.22210

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abstract = "A one-dimensional steady-state advection-diffusion problem using summation-by-parts operators is investigated. For approximating the second derivative, a wide stencil is used, which simplifies implementation and stability proofs. However, it also introduces spurious, oscillating, modes for all mesh sizes. We prove that the size of the spurious modes are equal to the size of the truncation error for a stable approximation and hence disappears with the convergence rate. The theoretical results are verified with numerical experiments.",

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Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative

Abstract

Keywords

ASJC Scopus subject areas

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