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Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in and , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive convergence without any convergence rate....
Finite element approximation for degenerate parabolic equations is
considered.
We propose a semidiscrete scheme provided with order-preserving
and L1 contraction properties, making use of piecewise linear
trial functions and the lumping mass technique.
Those properties allow us to apply nonlinear semigroup theory,
and the wellposedness and stability in L1 and L∞,
respectively, of the scheme are established.
Under certain hypotheses on the data, we also derive L1
convergence without any...
In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly...
We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to D hydrostatic Navier-Stokes equations.
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