Padesát let metody konečných prvků
Parallel fully coupled Schwarz preconditioners for saddle point problems.
Parallel implementation of Wavelet-Galerkin method
We present here some details of our implementation of Wavelet-Galerkin method for Poisson equation in C language parallelized by POSIX threads library and show its performance in dimensions .
Partition of unity method for Helmholtz equation: -convergence for plane-wave and wave-band local bases
In this paper we study the -version of the Partition of Unity Method for the Helmholtz equation. The method is obtained by employing the standard bilinear finite element basis on a mesh of quadrilaterals discretizing the domain as the Partition of Unity used to paste together local bases of special wave-functions employed at the mesh vertices. The main topic of the paper is the comparison of the performance of the method for two choices of local basis functions, namely a) plane-waves, and b) wave-bands....
Penalties, Lagrange multipliers and Nitsche mortaring
Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.
Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions
A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King...
Perturbation of mixed variational problems. Application to mixed finite element methods
Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes
Piecewise bilinear preconditioning of high-order finite element method.
Piecewise polynomial interpolations in the finite element method
Plane wave discontinuous Galerkin methods: Analysis of the h-version
We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane waves have been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that ...
Pointwise a posteriori error analysis for an adaptive penalty finite element method for the obstacle problem.
Pointwise error estimate for a noncoercive system of quasi-variational inequalities related to the management of energy production.
Pointwise Error Estimates for a Streamline Diffusion Finite Element Scheme.
Post-buckling range of plates in axial compression with uncertain initial geometric imperfections
The method of reliable solutions alias the worst scenario method is applied to the problem of von Kármán equations with uncertain initial deflection. Assuming two-mode initial and total deflections and using Galerkin approximations, the analysis leads to a system of two nonlinear algebraic equations with one or two uncertain parameters-amplitudes of initial deflections. Numerical examples involve (i) minimization of lower buckling loads and (ii) maximization of the maximal mean reduced stress.
Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems
In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of the mixed finite element space.
Postprocessing of a finite volume element method for semilinear parabolic problems
In this paper, we study a postprocessing procedure for improving accuracy of the finite volume element approximations of semilinear parabolic problems. The procedure amounts to solve a source problem on a coarser grid and then solve a linear elliptic problem on a finer grid after the time evolution is finished. We derive error estimates in the L2 and H1 norms for the standard finite volume element scheme and an improved error estimate in the H1 norm. Numerical results demonstrate the accuracy...
Postprocessing schemes for some mixed finite elements
Preconditioning conforming finite element methods for treating Dirichlet boundary conditions. II.
Preconditioning conforming finite element methods for treating Dirichlet boundary conditions. I.