A new paradigm for enriching virtual element methods
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We construct a virtual element method (VEM) based on approximation spaces that are enriched with special singular functions. This enriched VEM is tailored for the approximation of solutions to elliptic problems, which have singularities due to the geometry of the domain. Differently from the traditional extended Galerkin method approach, no partition of unity is employed. Rather, the design of the method hinges upon the special structure of the virtual element spaces. We present a full theoretical analysis of the method, supported by several numerical experiments.
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