Spline collocation for strongly elliptic equations on the torus.
Stabilité et convergence des méthodes spectrales polynômiales. Application à l'équation d'advection
Stability of microstructure for tetragonal to monoclinic martensitic transformations
We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...
Stabilization methods in relaxed micromagnetism
The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential and magnetization . In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming -element in spatial dimensions is shown to...
Stabilization methods in relaxed micromagnetism
The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential u and magnetization m. In [C. Carstensen and A. Prohl, Numer. Math.90 (2001) 65–99], the conforming P1 - (P0)d-element in d=2,3 spatial dimensions...
Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions.
Stable finite element methods for the Stokes problem.
Streamline diffusion finite element method for quasilinear elliptic problems.
Structure et estimations de coefficients d'erreurs
Structure et estimations de coefficients d'erreurs
Superconvergence analysis of approximate boundary-flux calculations.
Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations
We present a unified approach to studying the superconvergence property of the spectral volume (SV) method for high-order time-dependent partial differential equations using the local discontinuous Galerkin formulation. We choose the diffusion and third-order wave equations as our models to illustrate approach and the main idea. The SV scheme is designed with control volumes constructed using the Gauss points or Radau points in subintervals of the underlying meshes, which leads to two SV schemes...
Superconvergence of mixed finite element methods for parabolic equations
Sur une méthode d'éléments finis mixte pour l'équation biharmonique
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on , and meshes. It is shown that the combination FEM yields (up to a factor ) the same order of accuracy in the associated...
The Convergence of a Direct BEM for the Plane Mixed Boundary Value Problem of the Laplacian.
The difference method for non-linear elliptic differential equations with mixed derivatives
The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques (Short Communication)
The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.