A posteriori error estimates of characteristic mixed finite elements for convection-diffusion control problems

Abstract

In this article, we consider fully discrete characteristic mixed finite elements for convection-diffusion optimal control problems. We use the characteristic line method to treat the hyperbolic part of the state equation as a directional derivative. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. Using some proper duality problems, we derive a posteriori error estimates for the scalar functions. Such estimates are not available in the literature. A numerical example is presented to validate the theoretical results.

Keywords

• a posteriori error estimates
• characteristic mixed finite element methods
• convection-diffusion equations
• optimal control problems
• 49j20
• 65n30