Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces
Matrix transformation method of approximate solution of partial differential equations
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent norm are derived.
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.
Mixed approximation of eigenvalue problems: A superconvergence result
We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini...
Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization
This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution...
Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization
This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution...
Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems.
Monotone iterative technique for semilinear elliptic systems.
Monotone methods for solving a boundary value problem of second order discrete system.
Monotone scheme for finite difference equations concerning steady-state competing-species interactions
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy...
Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.