Three-points interfacial quadrature for geometrical source terms on nonuniform grids: Application to finite volume schemes for parameter-dependent differential equations

Theodoros Katsaounis, Chiara Simeoni*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which L p-error estimates, 1≤p<+∞, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics).

Original languageEnglish (US)
Pages (from-to)149-176
Number of pages28
JournalCalcolo
Volume49
Issue number3
DOIs
StatePublished - Sep 1 2012

Keywords

  • Consistency
  • Finite volume schemes
  • Geometrical source terms
  • Nonuniform grids
  • Optimal convergence rates

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

Fingerprint

Dive into the research topics of 'Three-points interfacial quadrature for geometrical source terms on nonuniform grids: Application to finite volume schemes for parameter-dependent differential equations'. Together they form a unique fingerprint.

Cite this