In this paper,an extremal eigenvalue problem to the Sturm-Liouville equations with discontinuous coefficients and volume constraint is investigated.Liouville transformation is applied to change the problem into an equivalent minimization problem.Finite element method is proposed and the convergence for the finite element solution is established.A monotonic decreasing algorithm is presented to solve the extremal eigenvalue problem.A global convergence for the algorithm in the continuous case is proved.A few numerical results are given to depict the efficiency of the method.
This paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system,namely recovering the unknown Neumann data on interior inaccessible boundary using Dirichlet measurement data on outer accessible boundary.Besides global upper and lower bounds established in[23],a posteriori local upper bounds and quasi-orthogonality results concerning the discretization errors of the state and adjoint variables are derived.Convergence and quasi-optimality of the proposed adaptive algorithm are rigorously proved.Numerical results are presented to illustrate the quasi-optimality of the proposed adaptive method.
