Abstract
A singularly perturbed parabolic equation of convection–diffusion type is examined. Initially the solution approximates a concentrated source. This causes an interior layer to form within the domain for all future times. Using a suitable transformation, a layer adapted mesh is constructed to track the movement of the centre of the interior layer. A parameter-uniform numerical method is then defined, by combining the backward Euler method and a simple upwinded finite difference operator with this layer-adapted mesh. Numerical results are presented to illustrate the theoretical error bounds established.
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