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Hamilton--Jacobi equations on an evolving surface. (arXiv:1810.03034v1 [math.NA])
来源于:arXiv
We consider the well-posedness and numerical approximation of a
Hamilton--Jacobi equation on an evolving hypersurface in $\mathbb R^3$.
Definitions of viscosity sub- and supersolutions are extended in a natural way
to evolving hypersurfaces and provide uniqueness by comparison. An explicit in
time monotone numerical approximation is derived on evolving interpolating
triangulated surfaces. The scheme relies on a finite volume discretisation
which does not require acute triangles. The scheme is shown to be stable and
consistent leading to an existence proof via the proof of convergence. Finally
an error bound is proved of the same order as in the flat stationary case. 查看全文>>