In this paper, we propose an interpolation based local postprocessing approach for finite element electronic structure calculations over locally refined hexahedral finite element meshes. It is shown that our approach ...
详细信息
ISBN:
(纸本)9783642113031
In this paper, we propose an interpolation based local postprocessing approach for finite element electronic structure calculations over locally refined hexahedral finite element meshes. It is shown that our approach is very efficient in finite element approximations of ground state energies.
Development of numerical methods for the solution of contact problems is a challenging task whose difficulty lies in the non-linear conditions for non-penetration and friction. Recently, many authors proposed to use v...
详细信息
Fluid-structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equ...
详细信息
ISBN:
(纸本)9783642113031
Fluid-structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation on the interface, involving the so-called Steklov-Poincare operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear sub-problems in the structure and the fluid domains. These sub-problems are spatially discretized by a finite element method on hybrid meshes containing different types of elements. For the time discretization implicit first-order methods are used for both sub-problems. The discretized equations are solved by algebraic multigrid methods.
For a Dirichlet problem for a singularly perturbed parabolic convection-diffusion equation with small parameter epsilon multiplying the highest-order derivative, a finite difference scheme with improved accuracy is co...
详细信息
ISBN:
(纸本)9783642196645
For a Dirichlet problem for a singularly perturbed parabolic convection-diffusion equation with small parameter epsilon multiplying the highest-order derivative, a finite difference scheme with improved accuracy is constructed that converges almost epsilon-uniformly with order of the convergence rate close to 2 for fixed values of epsilon. When constructing the scheme, monotone classical approximations of the differential equation on a priori adapted locally-uniform meshes are used. To improve accuracy of the scheme, the Richardson technique on embedded grids is applied.
In many scientific problems, adaptive finite element methods has been widely used to improve the accuracy of numerical solutions. The general idea is to refine or adjust the mesh such that the errors are "equally...
详细信息
暂无评论