The search session has expired. Please query the service again.
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...
We present a new method for generating a d-dimensional simplicial mesh
that minimizes the Lp-norm,
p > 0, of the interpolation error or its gradient. The method
uses edge-based error estimates to build a tensor metric. We describe and analyze the
basic steps of our method
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...
The accuracy of the domain embedding method from [A. Rieder, Modél. Math.
Anal. Numér.32 (1998) 405-431] for the solution of Dirichlet problems
suffers under a coarse boundary approximation. To overcome this drawback the method
is furnished with
an a priori (static) strategy for an adaptive approximation space refinement near the
boundary. This is done by selecting suitable wavelet subspaces.
Error estimates and
numerical experiments validate the proposed adaptive scheme.
In contrast to similar,...
Les méthodes sans maillage emploient une interpolation associée à un ensemble de particules : aucune information concernant la connectivité ne doit être fournie. Un des atouts de ces méthodes est que la discrétisation peut être enrichie d’une façon très simple, soit en augmentant le nombre de particules (analogue à la stratégie de raffinement ), soit en augmentant l’ordre de consistance (analogue à la stratégie de raffinement ). Néanmoins, le coût du calcul des fonctions d’interpolation est très...
Les méthodes sans maillage emploient une interpolation associée à un
ensemble de particules : aucune information concernant la connectivité ne doit être fournie.
Un des atouts de ces méthodes est que la discrétisation
peut être enrichie d'une
façon très simple, soit en augmentant le nombre de particules (analogue à la
stratégie de raffinement h), soit en augmentant l'ordre de consistance (analogue
à la stratégie de raffinement p). Néanmoins, le coût du calcul des fonctions
d'interpolation est...
The phase relaxation model is a diffuse interface model with
small parameter ε which
consists of a parabolic PDE for temperature
θ and an ODE with double obstacles
for phase variable χ.
To decouple the system a semi-explicit Euler method with variable
step-size τ is used for time discretization, which requires
the stability constraint τ ≤ ε. Conforming piecewise
linear finite elements over highly graded simplicial meshes
with parameter h are further employed for space discretization.
A posteriori...
For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.
Currently displaying 1 –
10 of
10