TY - JOUR
T1 - A Singularly Perturbed Convection-Diffusion Problem with a Moving Interior Layer
AU - J. L.Gracia & E. O'Riordan
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 823
EP - 843
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/661.html
KW - Singular perturbation, interior layer, Shishkin mesh.
AB - <p style="text-align: justify;">A singularly perturbed parabolic equation of convection-diffusion
type with an interior layer in the initial condition is studied. The solution
is decomposed into a discontinuous regular component, a continuous outflow
boundary layer component and a discontinuous interior layer component. A
priori parameter-explicit bounds are derived on the derivatives of these three
components. Based on these bounds, a parameter-uniform Shishkin mesh is
constructed for this problem. Numerical analysis is presented for the associated
numerical method, which concludes by showing that the numerical method is
a parameter-uniform numerical method. Numerical results are presented to
illustrate the theoretical bounds on the error established in the paper.</p>