### Abstract

Original language | English |
---|---|

Pages (from-to) | 493-512 |

Journal | Computational Methods in Applied Mathematics |

Volume | 3 |

Issue number | 3 |

Publication status | Published - 2003 |

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### Cite this

*Computational Methods in Applied Mathematics*,

*3*(3), 493-512.

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*Computational Methods in Applied Mathematics*, vol. 3, no. 3, pp. 493-512.

**On Convergence of the Exponentially Fitted Finite Volume Method with an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-Diffusion Equation.** / Wang, Song; Angermann, L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Convergence of the Exponentially Fitted Finite Volume Method with an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-Diffusion Equation

AU - Wang, Song

AU - Angermann, L.

PY - 2003

Y1 - 2003

N2 - This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.

AB - This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.

M3 - Article

VL - 3

SP - 493

EP - 512

JO - Computational Methods in Applied Mathematics

JF - Computational Methods in Applied Mathematics

SN - 1609-4840

IS - 3

ER -