A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

Mario Ohlberger

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 2, page 355-387
  • ISSN: 0764-583X

Abstract

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This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c t + ∇ · ( 𝐮 f ( c ) ) - ∇ · ( D ∇ c ) + λ c = 0 . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results.

How to cite

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Ohlberger, Mario. "A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations." ESAIM: Mathematical Modelling and Numerical Analysis 35.2 (2010): 355-387. <http://eudml.org/doc/197390>.

@article{Ohlberger2010,
abstract = { This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation $c_t + \nabla \cdot ( \{\bf u\}f(c)) - \nabla \cdot (D \nabla c) + \lambda c = 0$. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results. },
author = {Ohlberger, Mario},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {A posteriori error estimates; convection diffusion reaction equation; finite volume schemes; adaptive methods; unstructured grids.; a posteriori error estimates; finite volume schemes; unstructured grids; numerical experiments},
language = {eng},
month = {3},
number = {2},
pages = {355-387},
publisher = {EDP Sciences},
title = {A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations},
url = {http://eudml.org/doc/197390},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Ohlberger, Mario
TI - A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 355
EP - 387
AB - This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation $c_t + \nabla \cdot ( {\bf u}f(c)) - \nabla \cdot (D \nabla c) + \lambda c = 0$. The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability of the theoretical results.
LA - eng
KW - A posteriori error estimates; convection diffusion reaction equation; finite volume schemes; adaptive methods; unstructured grids.; a posteriori error estimates; finite volume schemes; unstructured grids; numerical experiments
UR - http://eudml.org/doc/197390
ER -

References

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