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.
The Treatment of Nonhomogeneous Dirichlet Boundary Conditions by the p-Version of the Finite Element Method.
The treatment of “pinching locking” in -shell elements
We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source...
The treatment of “pinching locking” in 3D-shell elements
We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of...
The Use of Infinite Grid Refinements at Singularities in the Solution of Laplace's Equation.
The use of linear approximation scheme for solving the Stefan problem
This paper deals with the linear approximation scheme to approximate a singular parabolic problem: the two-phase Stefan problem on a domain consisting of two components with imperfect contact. The results of some numerical experiments and comparisons are presented. The method was used to determine the temperature of steel in the process of continuous casting.
The use of semiregular finite elements
The virtual element method for eigenvalue problems with potential terms on polytopic meshes
We extend the conforming virtual element method (VEM) to the numerical resolution of eigenvalue problems with potential terms on a polytopic mesh. An important application is that of the Schrödinger equation with a pseudopotential term. This model is a fundamental element in the numerical resolution of more complex problems from the Density Functional Theory. The VEM is based on the construction of the discrete bilinear forms of the variational formulation through certain polynomial projection operators...
Total Flux Estimates for a Finite Element Approximation of the Dirichlet Problem Using the Boundary Penalty Method.
Toward the sinc-Galerkin method for the Poisson problem in one type of curvilinear coordinate domain.