Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems.
Distribution des résonances et décroissance de l’énergie locale pour le problème de transmission
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Divergence stability in connection with the -version of the finite element method
Domain decomposition algorithms for first-order system least squares methods.
Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes.
Domain optimization in -axisymmetric elliptic problems by dual finite element method
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
Domain optimization in axisymmetric elliptic boundary value problems by finite elements
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
Dorr, M.R.: Error Estimates for the Combined h and p Versions of the Finite Element Method.
Double resonance and multiple solutions for semilinear elliptic equations
Dual finite element analysis for elliptic problems with obstacles on the boundary. I
For an elliptic model problem with non-homogeneous unilateral boundary conditions, two dual variational formulations are presented and justified on the basis of a saddle point theorem. Using piecewise linear finite element models on the triangulation of the given domain, dual numerical procedures are proposed. By means of one-sided approximations, some a priori error estimates are proved, assuming that the solution is sufficiently smooth. A posteriori error estimates and two-sided bounds for the...
Dual finite element analysis for semi-coercive unilateral boundary value problems
Dual finite element analysis for unilateral boundary value problems
Dual finite element analysis of axisymmetric elliptic problems with an absolute term
A model second order elliptic equation in cylindrical coordinates with mixed boundary conditions is considered. A dual variational formulation is employed to calculate the cogradient of the solution directly. Approximations are defined on the basis of standard finite elements spaces. Convergence analysis and some a posteriori error estimates are presented.
Duality Estimates for the Numerical Solution of Integral Equations.
Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd
We consider the solution of second order elliptic PDEs in Rd with inhomogeneous Dirichlet data by means of an h–adaptive FEM with fixed polynomial order p ∈ N. As model example serves the Poisson equation with mixed Dirichlet–Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an H1 / 2–stable projection, for instance, the L2–projection for p = 1 or the Scott–Zhang projection for general p ≥ 1. For error estimation, we use a residual error estimator which...
Edge asymptotics on a skew cylinder: complex variable form
Effective solution of the Carleman problem for some groups of divergent type.
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...