Isoparametric Virtual Element Methods
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We present two approaches for constructing isoparametric Virtual Element Methods (IsoVEM) 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. They correspond to a Lagrangian and an Eulerian approach, respectively. Both methods are shown to converge optimally, a behaviour confirmed in practice for the solution of problems posed on curved domains. We envisage our analysis as a first step towards a rigorous treatment of problems posed on time-dependent domains and surface pdes.
