A posteriori finite element bounds with adaptive mesh refinement, application to outputs of the three dimensional convection-diffusion equation

grantor: University of TorontoNumerical simulations based on an 'a posteriori' finite element bound method with adaptive mesh refinement is presented for linear-functional outputs of the convection-diffusion equation in three spaces dimensions. The bound method is based upon the construction of an augmented Lagrangian, in which the objective is an energy reformulation of the desired output, and the constraints are the finite element equilibrium equations and inter-subdomain continuity requirements. Outputs are functionals of the field solution obtained from partial differential equations. The bound method provides relevant, quantitative, inexpensive. And rigorous bounds to the output on a very fine discretization at a cost of the coarse mesh calculation. To achieve a derived accuracy of the bound gap at a reasonable coat, an adaptive mesh refinement technique is used to refine the mesh only where high resolution is needed. Optimal stabilization parameter [kappa]* is also studied. This parameter improves the bounds, i.e. improves the sharpness of the bound gap. Finally the hybrid flux calculations on the coarse "working" mesh are compared with that on the fine "truth" mesh.M.A.Sc