Variational structure of the optimal artificial diffusion method for the advectiondiffusion equation

K. B. Nakshatrala, A. J. Valocchi

Research output: Contribution to journalArticlepeer-review

Abstract

In this research note, we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional (1D) problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advective-diffusive system, and then derive a new stable weak formulation. When applied to 1D problems with constant coefficients and forcing function, this resulting weak formulation will be equivalent to the optimal artificial diffusion method. We present representative numerical results to corroborate our theoretical findings.

Original languageEnglish (US)
Pages (from-to)559-572
Number of pages14
JournalInternational Journal of Computational Methods
Volume7
Issue number4
DOIs
StatePublished - Dec 2010

Keywords

  • EulerLagrange equations
  • Variational principles
  • advectiondiffusion equation
  • optimal artificial diffusion

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Computational Mathematics

Fingerprint Dive into the research topics of 'Variational structure of the optimal artificial diffusion method for the advectiondiffusion equation'. Together they form a unique fingerprint.

Cite this