Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type

Gracia, J.; O’Riordan, E.

doi:10.1090/mcom/2998

Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type
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by J. L. Gracia and E. O’Riordan PDF

Math. Comp. 85 (2016), 581-599 Request permission

Abstract:

Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh. A proof is given to show first order convergence of these numerical approximations in an appropriately weighted $C^1$-norm. Numerical results are given to illustrate the theoretical error bounds.

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