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.
On a variant of the local projection method stable in the SUPG norm
We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal projection with respect to a weighted inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
On additive scharz preconditioners for sparse grid discretizations.
On approximation of the Neumann problem by the penalty method
We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
On block diagonal and Schur complement preconditioning.
On Conforming Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations.
On discontinuous Galerkin method and semiregular family of triangulations
Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.
On equilibrium finite elements in three-dimensional case
The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.