TY - JOUR
T1 - A Posteriori Error Estimation for a Singularly Perturbed Problem with Two Small Parameters
AU - T. Linss
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 491
EP - 506
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/733.html
KW - Reaction-convection-diffusion problems, finite element methods, a posteriori error estimation, singular perturbation.
AB - <p style="text-align: justify;">A singularly perturbed two-point boundary-value problem of
reaction-convection-diffusion type is considered. The problem involves two
small parameters that give rise to two boundary layers of different widths.
The problem is solved using a streamline-diffusion FEM (SDFEM).<br/>A robust a posteriori error estimate in the maximum norm is derived. It provides
computable and guaranteed upper bounds for the discretisation error.<br/>Numerical examples are given that illustrate the theoretical findings and verify
the efficiency of the error estimator on a priori adapted meshes and in an
adaptive mesh movement algorithm.</p>