On a conjugate semi-variational method for parabolic equations
On a conjugate semi-variational method for parabolic equations
On a conservation upwind finite element scheme for convective diffusion equations
On a hierarchical basis multilevel method with nonconforming P1 elements.
On a method of two-sided eigenvalue estimates for elliptic equations of the form
The Collatz method of twosided eigenvalue estimates was extended by K. Rektorys in his monography Variational Methods to the case of differential equations of the form with elliptic operators. This method requires to solve, successively, certain boundary value problems. In the case of partial differential equations, these problems are to be solved approximately, as a rule, and this is the source of further errors. In the work, it is shown how to estimate these additional errors, or how to avoid...
On a Mixed Finite Element Approximation of the Stokes Problem (I). Convergence of the Approximate Solutions.
On a mixed finite element method for the Stokes problem in
On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian.
On a noncoercive system of quasi-variational inequalities related to stochastic control problems.
On a numerical model for diffusion-controlled growth and dissolution of spherical precipitates.
On a parallel implementation of the mortar element method
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
On a posteriori error estimators in the infinite element method on anisotropic meshes.
On a potential problem with incident wave as a field source
On a semi-variational method for parabolic equations. I
On a semi-variational method for parabolic equations. II
On a stabilized colocated Finite Volume scheme for the Stokes problem
We present and analyse in this paper a novel colocated Finite Volume scheme for the solution of the Stokes problem. It has been developed following two main ideas. On one hand, the discretization of the pressure gradient term is built as the discrete transposed of the velocity divergence term, the latter being evaluated using a natural finite volume approximation; this leads to a non-standard interpolation formula for the expression of the pressure on the edges of the control volumes. On the other...
On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local -superconvergence of the derivatives in the -norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.
On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.
On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate is proved in the -norm. For a class of polygonal domains the global estimate can be proven.