TY - JOUR
T1 - Interior Layers in a Reaction-Diffusion Equation with a Discontinuous Diffusion Coefficient
AU - C. de Falco & E. O'Riordan
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 444
EP - 461
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/730.html
KW - Diffusion Reaction Equations, Singularly Perturbed Differential Equations, Finite Difference Methods on Fitted Meshes.
AB - <p style="text-align: justify;">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 benefits
of using a piecewise-uniform Shishkin mesh over the use of uniform meshes in
the simulation of a simple semiconductor device.</p>