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.
Transfinite Element Methods: Blending-Function Interpolation over Arbitary Curved Element Domains.
Transonic flow calculation via finite elements
Using new results based on a convenient entropy condition, two types of algorithms for computing transonic flows are constructed. A sequence of solutions of the linearised problem with a posteriori control is constructed and its convergence to the physical solution of transonic flow in some special situations is proved. This paper contains also numerical results and their analysis for the case of flow past NACA 230012 airfoil. Some numerical improvements of the general algorithms, based on our...
Treatment of boundary singularities in two dimensional elliptic problems by Galerkin methods
Triangulation automatique d’un polyèdre en dimension
Třicet let matematické teorie metody konečných prvků (medailon prof. M. Zlámala)
Two Families of Mixed Finite Elements for Second Order Elliptic Problems.
Two preconditioners based on the multi-level splitting of finite element spaces.
Two simple derivations of universal bounds for the C.B.S. inequality constant
Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.
Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra.
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity uH computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that,...