Spectral analysis in connection with iterative solution of convection-diffusion equation.
Spectral approximation of variationally formulated eigenvalue problems on curved domains.
Spectral methods for singular perturbation problems
We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.
Spline collocation for strongly elliptic equations on the torus.
Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements
By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec’s edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements can...
Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements
By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec's edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free elements...
Stabilization methods of bubble type for the Q1/Q1-element applied to the incompressible Navier-Stokes equations
In this paper, a general technique is developed to enlarge the velocity space of the unstable -element by adding spaces such that for the extended pair the Babuska-Brezzi condition is satisfied. Examples of stable elements which can be derived in such a way imply the stability of the well-known Q2/Q1-element and the 4Q1/Q1-element. However, our new elements are much more cheaper. In particular, we shall see that more than half of the additional degrees of freedom when switching from the Q1...
Stabilization of Galerkin approximations of transport equations by subgrid modeling
Stabilization of Galerkin approximations of transport equations by subgrid modeling
This paper presents a stabilization technique for approximating transport equations. The key idea consists in introducing an artificial diffusion based on a two-level decomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method.
Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions.
Stable finite element methods for the Stokes problem.
Superconvergence analysis of approximate boundary-flux calculations.
Superconvergence by Steklov averaging in the finite element method
The Steklov postprocessing operator for the linear finite element method is studied. Superconvergence of order 𝓞(h²) is proved for a class of second order differential equations with zero Dirichlet boundary conditions for arbitrary space dimensions. Relations to other postprocessing and averaging schemes are discussed.
Superconvergence for rectangular mixed finite elements.
Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method
This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.
Superlinear CG convergence for special right-hand sides.
Sur la convergence des schémas aux différences finies pour des équations elliptiques du quatrième ordre avec des solutions irrégulières. (Convergence of finite difference schemes for fourth order elliptic equations with irregular solutions).
Sur la convergence numérique de différentes méthodes de décomposition pour une classe de problèmes elliptiques.
Sur l'approximation du problème de Dirichlet pour les opérateurs elliptiques d'ordre 2
Sur l'approximation numérique des écoulements quasi-newtoniens dont la viscosité suit la loi puissance ou la loi de Carreau