Fast Poisson Solvers on General Two Dimensional Regions for the Dirichlet Problem.
Fast solution of periodic integral equations by GMRES.
Fegen und Dünnheit mit Anwendungen auf die Laplace-und Wärmeleitungsgleichung
Several properties of balayage of measures in harmonic spaces are studied. In particular, characterisations of thinness of subsets are given. For the heat equation the following result is obtained: suppose that is given the presheaf of solutions ofand is a subset of satisfyingfor arbitrarily small. Then is thin at 0 if and only if is polar. Similar result for the Laplace equation. At last the reduced of measures is defined and several approximation theorems on reducing and balayage...
Finite Difference Approximations to the Dirichlet Problem for Elliptic Systems.
Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary
The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and -convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and -convergence proved for a regular solution. Some a posteriori error estimates are also presented.
Finite volume box schemes and mixed methods
Finite Volume Box Schemes and Mixed Methods
We present the numerical analysis on the Poisson problem of two mixed Petrov-Galerkin finite volume schemes for equations in divergence form . The first scheme, which has been introduced in [CITE], is a generalization in two dimensions of Keller's box-scheme. The second scheme is the dual of the first one, and is a cell-centered scheme for u and the flux φ. For the first scheme, the two trial finite element spaces are the nonconforming space of Crouzeix-Raviart for the primal unknown u...
Finite volume box schemes on triangular meshes
Finitude d'espaces d'états liés pour certains systèmes quantiques
Flatness of Domains and Doubling Properties of Measures Supported on their Boundary, with Applications to Harmonic Measure.
Formule de Poisson pour les variétés riemanniennes.
Fredholm property for a parameter dependent second order operator differential equation.
Free Boundary Problems with Nonlinear Source Terms.
From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions
There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations...
Functions of four variables which satisfy both the heat equation and the Laplace equation in three variables - II