Reliable and efficient error control for an adaptive Galerkin-characteristic method for convection-dominated diffusion problems

Authors:
Ming Cui;Zhangxin Chen;Richard E. Ewing;Guan Qin;Hongsen Chen
Affiliations:
School of Mathematics and System Science, Shandong University, Jinan, China 250100;Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Canada T2N 1N4;Institute for Scientific Computation, Texas A & M University, College Station, USA 77843-3404;Chemical and Petroleum Engineering Department, University of Wyoming, Laramie, USA 82071-3295;Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Canada T2N 1N4
Venue:
Advances in Computational Mathematics
Year:
2012

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Abstract

An efficient and reliable a-posteriori error estimator is developed for a characteristic-Galerkin finite element method for time-dependent convection-dominated problems. An adaptive algorithm with variable time and space steps is proposed and studied. At each time step in this algorithm grid coarsening occurs solely at the final iteration of the adaptive procedure, meaning that only time and space refinement is allowed before the final iteration. It is proved that at each time step this adaptive algorithm is capable of reducing errors below a given tolerance in a finite number of iteration steps. Numerical results are presented to check the theoretical analysis.