International journal for numerical methods in engineering vol:59 issue:15 pages:2065-2087
The necessity for a reliable measure of the discretization error arises in adaptive mesh refinement and in moving mesh adaptation. The present work discusses a detector of the discretization error based on the interpolation reconstruction of the operators. The technique presented here is named operator recovery error source detector (ORESD). Its main features are: First, the technique is based on the operators being discretized and does not require any user intervention or any a priori knowledge of the solution or its properties. Second, the ORESD is an a posteriori error indicator, but it is shown to be consistent with the a priori error provided by the modified equation approach. Third, the technique is based on the operators being solved and is tailored to the specific problem at hand. Four, the technique is simple and is based on a small stencil, resulting in a very inexpensive error detection.