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In this article, we provide a rigorous a priori error estimate for the symmetric coupling of the finite and boundary element method for the potential problem in three dimensions. Our theoretical framework allows an arbitrary number of poly-hedral subdomains. Our bound is not only explicit in the mesh parameter, but also in the subdomains themselves: the(More)
This paper presents the analysis of a distributed parabolic optimal control problem in a multiharmonic setting. In particular, the desired state is assumed to be multiharmonic. After eliminating the control from the optimality system, we arrive at the reduced optimality system for the state and the co-state that is nothing but a coupled system of a forward(More)
In the present paper, the solution of nonlinear elliptic boundary value problems (b.v.p.) on parallel machines with Multiple Instruction Multiple Data (MIMD) architecture is discussed. Especially, we consider electro{magnetic eld problems the numerical solution of which is based on nite element discretizations and a nested Newton solver. For solving the(More)
Poincaré type inequalities are a key tool in the analysis of partial differential equations. They play a particularly central role in the analysis of domain decomposition and multi-level iterative methods for second-order elliptic problems. When the diffusion coefficient varies within a subdomain or within a coarse grid element, then condition number bounds(More)
This work is devoted to fast and parameter-robust iterative solvers for frequency domain finite element equations, approximating the eddy current problem with harmonic excitation. We construct a preconditioned Min-Res solver for the frequency domain equations, that is robust (= parameter– independent) in both the discretization parameter h and the frequency(More)
This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lischitz and upper Hölder type,(More)
The use of the FEM and BEM in diierent subdomains of a non{overlapping Domain Decomposition (DD) and their coupling over the coupling boundaries (interfaces) brings about several advantages in many practical applications. The paper presents parallel solvers for large-scaled coupled FE{BE{DD equations approximating linear and nonlinear plane magnetic eld(More)
For the first biharmonic problem a mixed variational formulation is introduced which is equivalent to a standard primal variational formulation on arbitrary polygonal domains. Based on a Helmholtz decomposition for an involved nonstandard Sobolev space it is shown that the biharmonic problem is equivalent to three (consecutively to solve) second-order(More)
In this paper, we present and discuss the results of our numerical studies of preconditioned MinRes methods for solving the opti-mality systems arising from the multiharmonic finite element approximations to time-periodic eddy current optimal control problems in different settings including different observation and control regions, different tracking terms(More)