A remark to the finite element method
A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity
In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities...
A residual based A POSTERIORI error estimator for an augmented mixed finite element method in linear elasticity
In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities...
A review of two different approaches for superconvergence analysis
In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.
A Right-Inverse for the Divergence Operator in Spaces of Piecewise Polynomials. Application to the p-Version of the Finite Element Method
A Ritz method based on a complementary variational principle
A robust and parallel multigrid method for convection diffusion equations.
A Second Order Splitting Method for the Cahn-Hilliard Equation.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H1-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver
A shock-capturing discontinuous Galerkin method for the numerical solution of inviscid compressible flow
A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations
The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.
A special finite element method based on component mode synthesis
The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
A spectral-Tau approximation for the Stokes and Navier-Stokes equations
A Stability Analysis for the Extended Kantorovich Method Applied to the Torsion Problem.
A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes
It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior...
A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in Elastostatics
In this work we consider a stabilized Lagrange multiplier method in order to approximate the Coulomb frictional contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed. We study the existence and the uniqueness of solution of the discrete problem.