The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
In this article, we consider the initial value problem which is obtained
after a space discretization (with space step )
of the equations governing the solidification process of
a multicomponent alloy.
We propose a numerical scheme to solve numerically this initial value
problem. We prove an error estimate which is not affected by
the step size chosen in the space discretization. Consequently, our scheme
provides global convergence without any stability condition between and
the time...
The present paper deals with a finite element approximation of partial differential equations when the
domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming
because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized.
We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
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