Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions.
Stable finite element methods for the Stokes problem.
Streamline diffusion finite element method for quasilinear elliptic problems.
Structure et estimations de coefficients d'erreurs
Structure et estimations de coefficients d'erreurs
Superconvergence analysis of approximate boundary-flux calculations.
Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations
We present a unified approach to studying the superconvergence property of the spectral volume (SV) method for high-order time-dependent partial differential equations using the local discontinuous Galerkin formulation. We choose the diffusion and third-order wave equations as our models to illustrate approach and the main idea. The SV scheme is designed with control volumes constructed using the Gauss points or Radau points in subintervals of the underlying meshes, which leads to two SV schemes...
Superconvergence of mixed finite element methods for parabolic equations
Sur une méthode d'éléments finis mixte pour l'équation biharmonique
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on , and meshes. It is shown that the combination FEM yields (up to a factor ) the same order of accuracy in the associated...
The Convergence of a Direct BEM for the Plane Mixed Boundary Value Problem of the Laplacian.
The difference method for non-linear elliptic differential equations with mixed derivatives
The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques (Short Communication)
The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
The Finite Element Method for Parabolic Equations. I. A Posteriori Error Estimation
The Finite Element Method for Parabolic Equations. II. A Posteriori Error Estimation and Adaptive Approach
The Finite Element Method with Lagrangian Multipliers.
The Finite Element Method with Non-Uniform Mesh Sizes Applied to the Exterior Helmholtz Problem.