Identifying Parameters In Convection Diffusion Equations

In this thesis,we shall reconstruct the convection velocity and source simulta-neously in the convection diffusion equation from the extra measurement in the ?.We assume the extra measurement data is available in ? which is an open bounded subset of ?.The ill-posed inverse problem is formulated into an output least-squares nonlinear and non-convex minimization with Tikhonov regularization.First,the ex-istence of optimal solution to the minimization of the cost functional is proven,and the convergence of the approximation is showed for the regularization.Then a simple finite element method is used to approximate the constrained minimization prob-lem.Finally,the convergence of the finite-element solution to the minimizer of the continuous optimization problem is shown in the last section.