A singularly perturbed convection-diffusion problem with a moving pulse

作者：Gracia J L; O'Riordan E^*

来源：Journal of Computational and Applied Mathematics, 2017, 321: 371-388.

DOI：10.1016/j.cam.2017.03.003

• Singular perturbation
• Gaussian pulse
• Shishkin mesh

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.

• 出版日期2017-9