A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection-dominated diffusion equation

Authors:
Ningning Yan;Zhaojie Zhou
Affiliations:
Institute of Systems Science, Academy of Mathematics and System Science, Chinese Academy of Science, Beijing 10080, China;Institute of Systems Science, Academy of Mathematics and System Science, Chinese Academy of Science, Beijing 10080, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we study an edge-stabilization Galerkin approximation scheme for the constrained optimal-control problem governed by convection-dominated diffusion equation. The method uses least-square stabilization of the gradient jumps across element edges. A priori and a posteriori error estimates are derived for both the state, co-state and the control. The theoretical results are illustrated by two numerical experiments.