An Efficient DWR-Type a Posteriori Error Bound of SDFEM for Singularly Perturbed Convection-Diffusion PDEs

Abstract: The main target of this research is to provide an efficient   residual-based a posteriori error bound in the standard energy norm   for the streamline-diffusion finite element method (SDFEM) devoted to   the stationary convection-diffusion equations. To improve the accuracy   of this estimator, we weighted the estimator through some relevant   factors obtained by using the solution of the corresponding dual   problem. Finally, we contribute a new computable DWR-type robust a   posteriori error estimator to the literature of SDFEM. Also, we   establish the lower bound for the local estimator. Lastly, the   proposed method is justified by some numerical experiments, and   several future scopes related to this work are also addressed.