On the equivalence of primal and dual substructuring preconditioners.
On the evaluation of finite element sensitivities to nodal coordinates.
On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs
The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space , on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space .
On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary
In this note we present an algorithm for a construction of strongly regular families of triangulations for planar domains with a piecewise curved boundary. Some additional properties of the resulting triangulations are considered.
On the Extrapolation of Galerkin Methods for Parabolic Problems.
On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical...
On the Finite Element Approximation of a Cascade Flow Problem.
On the finite element approximation of solutions for radiation problem
On the Finite Element Method.
On the finite volume element method.
On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.
On the Multigrid Solution of Finite Element Equations With Isoparametric Elements.
On the Multi-Level Splitting of Finite Element Squares.
On the Newton-Kantorovich theorem and nonlinear finite element methods
Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.
On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.
On the Numerical Approximation of Finite Speed Diffusion Problems.
On the numerical approximation of first-order Hamilton-Jacobi equations
Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
On the numerical modeling of deformations of pressurized martensitic thin films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.
On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems
Karátson and Korotov developed a sharp upper global a posteriori error estimator for a large class of nonlinear problems of elliptic type, see J. Karátson, S. Korotov (2009). The goal of this paper is to check its numerical performance, and to demonstrate the efficiency and accuracy of this estimator on the base of quasilinear elliptic equations of the second order. The focus will be on the technical and numerical aspects and on the components of the error estimation, especially on the adequate...