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,...
The nonconforming finite element method in the problem of clamped plate with ribs
The numerical solution of large finite element systems by explicit preconditioning semi-direct methods
The Numerical Solutions of Interface Problems by Infinite Element Method.
The -version of the finite element method for elliptic equations of order
The pseudospectral method for thermotropic primitive equation and its error estimation.
The response of skin friction, wall heat transfer and pressure drop to wall waviness in the presence of buoyancy.
The role of Sommerville tetrahedra in numerical mathematics
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by...
The second order projection method in time for the time-dependent natural convection problem
We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is...
The Sinc Method in Multiple Space Dimensions: Model Probelms.
The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type
In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some error estimates for finite element methods for parabolic integro-differential equations.
The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions
We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.