Isoparametric Virtual Element Methods
CoRR(2024)
摘要
We present two approaches to constructing isoparametric Virtual Element
Methods of arbitrary order for linear elliptic partial differential equations
on general two-dimensional domains. The first method approximates the
variational problem transformed onto a computational reference domain. The
second method computes a virtual domain and uses bespoke polynomial
approximation operators to construct a computable method. Both methods are
shown to converge optimally, a behaviour confirmed in practice for the solution
of problems posed on curved domains.
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