505 research outputs found

    Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient

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    In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction–diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter–uniform methods based on piecewise–uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the beneïŹts of using a piecewise–uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device

    Mini-Workshop: Finite Elements and Layer Adapted Meshes

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    [no abstract available

    Robust Numerical Methods for Singularly Perturbed Differential Equations--Supplements

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    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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