An upwind finite element method for singularly perturbed elliptic problems and local estimates in the -norm
Analyse d'un élément mixte pour le problème de Stokes . I. Résultats générauax.
Analyse d'un élément mixte pour le problème de Stokes . II. Construction et estimations d'erreur.
Analyse numérique des écoulements quasi-Newtoniens dont la viscosité obéit à la loi puissance ou la loi de carreau.
Analysis of a new augmented mixed finite element method for linear elasticity allowing -- approximations
We present a new stabilized mixed finite element method for the linear elasticity problem in . The approach is based on the introduction of Galerkin least-squares terms arising from the constitutive and equilibrium equations, and from the relation defining the rotation in terms of the displacement. We show that the resulting augmented variational formulation and the associated Galerkin scheme are well posed, and that the latter becomes locking-free and asymptotically locking-free for Dirichlet...
Analysis of a non-standard mixed finite element method with applications to superconvergence
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent. Superconvergence of the latter was earlier investigated by Brandts, Chen and Yang between 2004 and 2006. Since the new method leads to a non-symmetric system matrix, its application seems however more expensive...
Analysis of a quasicontinuum method in one dimension
The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long-range interactions and a QC formulation which incorporates several important aspects of practical QC methods. First, we prove the existence, the local uniqueness...
Analysis of Finite Element Methods for Second Order Boundary Value Problems Using Mesh Dependent Norms.
Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D
So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
Analysis of mixed finite element methods on locally refined grids.
Analysis of mixed methods using conforming and nonconforming finite element methods
Analysis of parabolic difference schemes by Gerschgorin's method
Analysis of the potential formulation for the eddy current problem in a bounded domain.
Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition
The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin methods. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown that due to...
Anisotropic -adaptive method based on interpolation error estimates in the -seminorm
We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken -seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of the proposed...
Anisotropic mesh adaption: application to computational fluid dynamics
In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems...
Anisotropic mesh refinement in polyhedral domains: error estimates with data in L2(Ω)
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant...
Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods
In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, and . Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.
Approximation d'un problème aux limites elliptique d'ordre deux par éléments finis rationnels de Wachspress avec intégration numérique
Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology
The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results...