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ALE-type FEM formulation for PDEs on time-dependent domains with vanishing discrete SCL. (arXiv:1809.06553v1 [math.NA])
来源于:arXiv
The aim of this paper is to introduce a finite element formulation within
Arbitrary Lagrangian Eulerian framework with vanishing discrete {\it Space
Conservation Law} (SCL) for differential equations on time dependent domains.
The novelty of the formulation is the method for temporal integration which
results in preserving the SCL property and retaining the higher order accuracy
at the same time. Once the time derivative is discretized (based on integration
or differentiation formula), the common approach for terms in differential
equation which do not involve temporal derivative is classified to be a kind of
"time averaging" between time steps. In the spirit of classical approaches,
this involves evaluating these terms in several points in time between the
current and the previous time step ($[t_n,t_{n+1}]$), and then averaging them
in order to provide the satisfaction of discrete SCL. Here, we fully use the
polynomial in time form of mapping through which evolution of domain is
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