In this paper, we construct a semi-discrete scheme and a fully discrete scheme using the Wilson nonconforming element for the parabolic integro-differential equation arising in modeling the non-Fickian flow in porous media by the interior penalty method. Without using the conventional elliptic projection, which was an indispensable tool in the convergence analysis of finite element methods in p...

We discuss the implementation of hybrid finite element methods in the Distributed and Unified Numerics Environment (DUNE). Such hybrid methods require the approximation of the solution in the interior of the elements, as well as an approximation of the traces of the solution on the element interfaces, i.e., the skeleton. For illustration, we consider a hybrid version of the interior penalty dis...

ABSTRACT In this talk we will discuss a nonoverlapping domain decomposition preconditioner for the weakly over-penalized symmetric interior penalty (WOPSIP) method. The WOPSIP method belongs to the family of discontinuous finite element methods. The preconditioner for the WOPSIP method is based on the balancing domain decomposition by constraints methodology. Theoretical results on the conditio...

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a...

A continuous interior penalty hp-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an hp-inverse trace inequality, a local discontinuous to continuous hp-interpola...

The goal of this paper is to establish exponential convergence of hp-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the conver...

We introduce a Nitsche-based formulation for the finite element discretization of the unilateral contact problem in linear elasticity. It features a weak treatment of the non-linear contact conditions through a consistent penalty term. Without any additional assumption on the contact set, we can prove theoretically its fully optimal convergence rate in the H(Ω)norm for linear finite elements in...

This work presents the coupling of two locally conservative methods for elliptic problems: namely, the discontinuous Galerkin method and the mixed finite element method. The couplings can be defined with or without interface Lagrange multipliers. The formulations are shown to be equivalent. Optimal error estimates are given; penalty terms may or may not be included. In addition, the analysis fo...

We present multigrid methods for a biharmonic problem with boundary conditions of the Cahn-Hilliard type. These multigrid methods are based on discretizations obtained by a quadratic C interior penalty method. Since the finite element space is a standard space for second order problems, multigrid solves for second order problems can be used naturally in the smoothing steps. We will present theo...

in this paper, single, bi-layered and three-layered tube hydroforming processes were numerically simulated using the finite element method. it was found that the final bulges heights resulted from the models were in good agreement with the experimental results. three types of modeling were kept with the same geometry, tube material and process parameters to be compared between the obtained hydr...