505 research outputs found
Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient
In this paper a problem arising in the modelling of semiconductor
devices motivates the study of singularly perturbed differential equations of reactionâdiffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameterâuniform methods based on piecewiseâuniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the beneïŹts of using a piecewiseâuniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device
Mini-Workshop: Finite Elements and Layer Adapted Meshes
[no abstract available
Robust Numerical Methods for Singularly Perturbed Differential Equations--Supplements
The second edition of the book "Roos, Stynes, Tobiska -- Robust Numerical
Methods for Singularly Perturbed Differential Equations" appeared many years
ago and was for many years a reliable guide into the world of numerical methods
for singularly perturbed problems. Since then many new results came into the
game, we present some selected ones and the related sources.Comment: arXiv admin note: text overlap with arXiv:1909.0827
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