Über den ersten Eigenwert des Laplace-Operators auf kompakten Riemannschen Flächen
Über die punktweise Konvergenz Finiter Elemente. - On the Pointwise Convergence of Finite Elements.
Über eine Eigenschaft der verallgemeinerten Lösung des Poissonschen Problems (Vorläufige Mitteilung)
Über Membranen mit speziellen Knotenlinien.
Ueber die Eigenwerte des Laplace-Operators auf kompakten Riemannschen Flächen II.
Une méthode d'éléments finis hybrides en décomposition de domaines
Une méthode intégrale de frontière. Application au Laplacien et à l'élasticité.
The aim of the paper is to give a method to solve boundary value problems associated to the Helmholtz equation and to the operator of elasticity. We transform these problems in problems on the boundary Gamma of an open set of R3. After introducing a symplectic form on H1,2(G) x H-1,2(G) we obtain the adjoint of the boundary operator employed. Then the boundary problem has a solution if and only if the boundary conditions are orthogonal, for this bilinear form, to the elements of the kernel, in a...
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...
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...
Uniqueness and Free Interpolation for Logarithmic Potentials and the Cauchy Problem for the Laplace Equation in R2.
Uniqueness of critical points for semi-linear Dirichlet problems in convex domains.
Uniqueness of Dirichlet, Neumann, and mixed boundary value problems for Laplace's and Poisson's equations for a rectangle.