Singular solutions of a transmission problem in plane linear elasticity for wedge-shaped regions.
Singularities in two- and three-dimensional elliptic problems and finite element methods for their treatment
Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...
Small-stencil 3D schemes for diffusive flows in porous media
In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.
Small-stencil 3D schemes for diffusive flows in porous media
In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.
Smoothed prolongation multigrid with rapid coarsening and massive smoothing
We prove that within the frame of smoothed prolongations, rapid coarsening between first two levels can be compensated by massive prolongation smoothing and pre- and post-smoothing derived from the prolongator smoother.
Solution of a class of quasilinear Dirichlet and Neumann problems by the method of reduction.
Solution of a class of quasilinear Dirichlet and Neumann problems by the method of reduction. (Short Communication).
Solutions stables d'un problème simplifié de coque élastique
Some asymptotic error estimates for finite element approximation of minimal surfaces
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...
Some equilibrium and mixed models in the finite element method
Some Equilibrium Finite Element Methods for Two- Dimensional Elasticity Problems.
Some -error estimates for semi-variational method applied to parabolic equations
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some new convergence results in finite element theories for elliptic problems
Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method
We consider a family of conforming finite element schemes with piecewise polynomial space of degree in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is in the discrete norms of and , where and are the mesh size of the spatial and temporal discretization, respectively....
Some New Families of Finite Elements for the Stokes Equations.
Some nonstandard finite element estimates with applications to Poisson and Signorini problems.