Optimal design of stationary flow problems by path-following interior-point methods
Multi-Grid Methods for Hamiltonian-Jacobi-Bellmann Equations.
Numerical simulation of surface acoustic wave actuated cell sorting
We consider the mathematical modeling and numerical simulation of high throughput sorting of two different types of biological cells (type I and type II) by a biomedical micro-electro-mechanical system (BioMEMS) whose operating behavior relies on surface acoustic wave (SAW) manipulated fluid flow in a microchannel. The BioMEMS consists of a separation channel with three inflow channels for injection of the carrier fluid and the cells, two outflow channels for separation, and an interdigital transducer...
Preface
Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a...
Une méthode multigrille pour la solution des problèmes d'obstacle
Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation
For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created edges/nodal...
An error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator and provide a bulk...
Residual based a posteriori error estimators for eddy current computation
We consider ;Ω)-elliptic problems that have been discretized by means of Nédélec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as error estimators to control adaptive refinement. Under certain assumptions on material parameters and computational domains, we derive local lower bounds and a global upper bound for the total error measured in the energy norm. The...
Residual based a posteriori error estimators for eddy current computation
Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation
For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created edges/nodal...
An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
Page 1