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Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method

Pengzhan Huang (2014)

Applications of Mathematics

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.

Superconvergence of external approximation for two-point boundary problems

Teresa Regińska (1987)

Aplikace matematiky

The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.

Supersolutions and stabilization of the solutions of the equation∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u), Part II.

Abderrahmane El Hachimi, François De Thélin (1991)

Publicacions Matemàtiques

In this paper we consider a nonlinear parabolic equation of the following type:(P)      ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u)with Dirichlet boundary conditions and initial data in the case when 1 < p < 2.We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with (P).

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