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Numerical methods for convection-diffusion problems with layers

Published on:

1 November 2023

Primary Category:

Numerical Analysis

Paper Authors:

Alan F. Hegarty,

Eugene O'Riordan


Key Details

Uses fitted finite elements on a Shishkin mesh for a 2D convection-diffusion equation

Test functions are exponential splines in one direction, combined with bilinear trial functions

Achieves higher order convergence compared to just using upwinding

Is a parameter-uniform method that handles boundary and corner layers

Stability and convergence analysis proves order N^-2 log(N)^2

AI generated summary

Numerical methods for convection-diffusion problems with layers

This paper develops a numerical method to solve a 2D convection-diffusion equation that can have multiple boundary and corner layers in the solution. It uses a fitted finite element method on a Shishkin mesh, with exponential splines as test functions in one direction. Analysis shows the method is stable, achieves higher order convergence, and is parameter-uniform.

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