TY - JOUR
T1 - A Posteriori Error Estimation for a Defect-Correction Method Applied to Convection-Diffusion Problems
AU - T. Linss & N. Kopteva
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 718
EP - 733
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/748.html
KW - Convection-diffusion problems, finite difference schemes, defect correction, a posteriori error estimation, singular perturbation.
AB - <p style="text-align: justify;">We consider a two-point boundary-value problem for a singularly
perturbed convection-diffusion problem. The problem is solved by using a
defect-correction method based on a first-order upwind difference scheme and
a second-order (unstabilized) central difference scheme.<br/>A robust a posteriori error estimate in the maximum norm is derived. It
provides computable and guaranteed upper bounds for the discretization error.
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>