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The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous...
Les méthodes sans maillage emploient une interpolation associée à un ensemble de particules : aucune information concernant la connectivité ne doit être fournie. Un des atouts de ces méthodes est que la discrétisation peut être enrichie d’une façon très simple, soit en augmentant le nombre de particules (analogue à la stratégie de raffinement ), soit en augmentant l’ordre de consistance (analogue à la stratégie de raffinement ). Néanmoins, le coût du calcul des fonctions d’interpolation est très...
Les méthodes sans maillage emploient une interpolation associée à un
ensemble de particules : aucune information concernant la connectivité ne doit être fournie.
Un des atouts de ces méthodes est que la discrétisation
peut être enrichie d'une
façon très simple, soit en augmentant le nombre de particules (analogue à la
stratégie de raffinement h), soit en augmentant l'ordre de consistance (analogue
à la stratégie de raffinement p). Néanmoins, le coût du calcul des fonctions
d'interpolation est...
We consider the lowest-order Raviart–Thomas mixed finite element
method for second-order elliptic problems on simplicial meshes in
two and three space dimensions. This method produces saddle-point
problems for scalar and flux unknowns. We show how to easily and
locally eliminate the flux unknowns, which implies the equivalence
between this method and a particular multi-point finite volume
scheme, without any approximate numerical integration. The matrix
of the final linear system is sparse, positive...
The phase relaxation model is a diffuse interface model with
small parameter ε which
consists of a parabolic PDE for temperature
θ and an ODE with double obstacles
for phase variable χ.
To decouple the system a semi-explicit Euler method with variable
step-size τ is used for time discretization, which requires
the stability constraint τ ≤ ε. Conforming piecewise
linear finite elements over highly graded simplicial meshes
with parameter h are further employed for space discretization.
A posteriori...
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
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