An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems

An Adaptive Finite Element Method for Nonlinear Optimal Control Problems

An Adaptive Finite Element Method for Linear Elliptic Problems

We propose an adaptive finite element method for linear elliptic problems based on an optimal maximum norm error estimate. The algorithm produces a sequence of successively refined meshes with a final mesh on which a given error tolerance is satisfied. In each step the refinement to be made is determined by locally estimating the size of certain derivatives of the exact solution through compute...

An explicit Wave Based - Finite element model as alterna- tive to the DtN finite element method

The solution of unbounded Helmholtz problems is the subject of substantial research. If these problems are to be solved using a domain-based discretisation technique like the finite element method (FEM), the computational domain has to be truncated to a bounded region. The unbounded nature of the problem exterior to this truncation is simulated by an appropriate condition on the truncation. A c...

An Adaptive Finite Element Method

We develop an adaptive nite element algorithm for reactive ow simulations. The underlying equations are the Navier-Stokes equations for low-Mach-number ows and an additional system of convection-diiusion-reaction equations for the chemical species. Especially in combustion problems the reaction terms are very stii and nonlinear. This set of equations represents a complicated system of PDEs whic...

An adaptive finite element method for magnetohydrodynamics

We describe a procedure for the adaptive h-refinement solution of the incompressible MHD equations in stream function form using a stabilized finite element formulation. The mesh is adapted based on a posteriori spatial error estimates of the magnetic field using both recovery and order extrapolation techniques. The step size for time integration is chosen so that temporal discretization errors...