Combined finite element -- finite volume method (convergence analysis)

Mária Lukáčová-Medviďová

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 4, page 717-741
  • ISSN: 0010-2628

Abstract

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We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion equation. We prove the convergence of the numerical solution to the exact solution.

How to cite

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Lukáčová-Medviďová, Mária. "Combined finite element -- finite volume method (convergence analysis)." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 717-741. <http://eudml.org/doc/248092>.

@article{Lukáčová1997,
abstract = {We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion equation. We prove the convergence of the numerical solution to the exact solution.},
author = {Lukáčová-Medviďová, Mária},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compressible Navier-Stokes equations; nonlinear convection-diffusion equation; finite volume schemes; finite element method; numerical integration; apriori estimates; convergence of the scheme; nonlinear convection-diffusion equation; finite element method; finite volume scheme; a priori estimates; convergence of the numerical method},
language = {eng},
number = {4},
pages = {717-741},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Combined finite element -- finite volume method (convergence analysis)},
url = {http://eudml.org/doc/248092},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Lukáčová-Medviďová, Mária
TI - Combined finite element -- finite volume method (convergence analysis)
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 4
SP - 717
EP - 741
AB - We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion equation. We prove the convergence of the numerical solution to the exact solution.
LA - eng
KW - compressible Navier-Stokes equations; nonlinear convection-diffusion equation; finite volume schemes; finite element method; numerical integration; apriori estimates; convergence of the scheme; nonlinear convection-diffusion equation; finite element method; finite volume scheme; a priori estimates; convergence of the numerical method
UR - http://eudml.org/doc/248092
ER -

References

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