Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
We prove quasi-optimality of an adaptive finite element algorithm for a model problem of optimal control including control constraints. The quasi-optimility expresses the fact that the decrease of error with respect to the number of mesh cells is optimal up to a constant. The considered algorithm is based on an adaptive marking strategy which compares a standard residualtype a posteriori error estimator with a data approximation term in each step of the algorithm in order to adapt the marking of cells.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
In this paper, we discuss a new iterative method for computing sinp. This function was introduced by Lindqvist in connection with the unidimensional nonlinear Dirichlet eigenvalue problem for the p-Laplacian. The iterative technique was inspired by the inverse power method in finite dimensional linear algebra and is competitive with other methods available in the literature. Keywords: p-Laplacian, eigenvalues, eigenfunctions, sinp, inverse power method.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
We address the coupling of an advection equation with a diffusion-advection equation, for solutions featuring boundary layers. We consider non-overlapping domain decompositions and we face up the heterogeneous problem using an extended variational formulation. We will prove the equivalence between the latter formulation and a treatment based on a singular perturbation theory. An exhaustive comparison in terms of solution and computational efficiency between these formulations is carried out.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
A conforming finite element discretization of the pure traction elasticity boundary value problem results in a singular linear system of equations. The singularity of the linear system is removed through various approaches. In this report, we consider an alternative approach in which discrete finite element formulations are derived directly from the principle of minimum potential energy. This point of view turns out to be particularly well suited to handle the rigid body modes, which are the source of the singularity in the finite element linear system. Our approach allows us to formulate a regularized potential energy principle and show that the associated weak problem is coercive in H1(Ω). This guarantees nonsingular problems, enables simplified solution algorithms and leads to more efficient and robust preconditioners for the iterative solution linear equations.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
We are interested in closed loop feedback control laws for supply chains. The mathematical modeling is based on Boltzmann–type equations. These equations allow to model a supply chain with priorities. The latter influence the processing time in a nonlinear way. For this class of models we derive a control law and we show numerical results.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
In this paper we consider a posteriori error estimates for space-time finite element discretizations for optimal control of hyperbolic partial dierential equations of second order. It is an extension of Meidner and Vexler (2007), where optimal control problems of parabolic equations are analyzed. The state equation is formulated as a first order system in time and a posteriori error estimates are derived separating the in uences of time, space, and control discretization. Using this information the accuracy of the solution is improved by local mesh refinement. Numerical examples are presented. Finally, we analyze the conservation of energy of the homogeneous wave equation with respect to dynamically in time changing spatial meshes.
Unable to retrieve citations for this document
Retrieving citations for document...
Open Access
January 1, 2011
Abstract
Domain decomposition methods are used for the approximate solution of boundary-value problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are fully taken into account in iteration-free domain decomposition schemes. Regionally-additive schemes are based on various classes of splitting schemes. In this paper we highlight a class of domain decomposition schemes which are based on the partition of the initial domain into subdomains with common boundary nodes. Using a partition of unity we construct and analyze unconditionally stable schemes for domain decomposition based on a two-component splitting: the problem within each subdomain and the problem at their boundaries. As an example we consider a Cauchy problem of first or second order in time with a non-negative self-adjoint second order operator in space. The theoretical discussion is supplemented with the numerical solution of a model problem for a two-dimensional parabolic equation.