Abstract
An optimal control problem for the advection-diffusion equation is studied using a Lagrangian-moving mesh finite element method. The weak formulation of the model advection---diffusion equation is based on Lagrangian coordinates, and semi---discrete (in space) error estimates are derived under minimal regularity assumptions. In addition, using these estimates and Brezzi-Rappaz-Raviart theory, symmetric error estimates for the optimality system are derived. The results also apply for advection dominated problems
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