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.
The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
The finite element solution of parabolic equations
In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in -dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in -norm of the method.
The finite element solution of second order elliptic problems with the Newton boundary condition
The convergence of the finite element solution for the second order elliptic problem in the -dimensional bounded domain with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the and norms are obtained.
The general form of local bilinear functions
The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces and is given.
The generalized finite volume SUSHI scheme for the discretization of the peaceman model
We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later,...
The version of the finite element method with quasiuniform meshes
The Hierarchical Basis Multigrid Method.
The hierarchical basis multigrid method for convection-diffusion equations.
The h-p Version of the Finite Element Method for Elliptic Equations of Order 2m.
The Indicatrix Method in Free Boundary Problems.
The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements
A reference triangular quadratic Lagrange finite element consists of a right triangle with unit legs , , a local space of quadratic polynomials on and of parameters relating the values in the vertices and midpoints of sides of to every function from . Any isoparametric triangular quadratic Lagrange finite element is determined by an invertible isoparametric mapping . We explicitly describe such invertible isoparametric mappings for which the images , of the segments , are segments,...
The mortar element method for three dimensional finite elements
The Mortar finite element method for Bingham fluids
This paper deals with the flow problem of a viscous plastic fluid in a cylindrical pipe. In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method. By using appropriate techniques, we are able to prove the convergence of the method and to obtain the same convergence rate as in the conforming case.
The mortar finite element method for Bingham fluids
This paper deals with the flow problem of a viscous plastic fluid in a cylindrical pipe. In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method. By using appropriate techniques, we are able to prove the convergence of the method and to obtain the same convergence rate as in the conforming case.
The Mortar method in the wavelet context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
The Mortar Method in the Wavelet Context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...