
Nonconforming Virtual Element Method for 2mth Order Partial Differential Equations in R^n with m>n
The H^mnonconforming virtual elements of any order k on any shape of po...
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Anisotropic H_divnorm error estimates for rectangular H_divelements
For the discretisation of H_divfunctions on rectangular meshes there ar...
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Optimal maximum norm estimates for virtual element methods
The maximum norm error estimations for virtual element methods are studi...
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H^2 Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model
We establish a new H2 Korn's inequality and its discrete analog, which g...
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An enhanced VEM formulation for plane elasticity
In this paper, an enhanced Virtual Element Method (VEM) formulation is p...
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Optimization of Virtual Networks
We introduce a general and comprehensive model for the design and optimi...
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General polytopial H(div) conformal finite elements and their discretisation spaces
We present a class of discretisation spaces and H(div)conformal element...
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H^mConforming Virtual Elements in Arbitrary Dimension
The H^mconforming virtual elements of any degree k on any shape of polytope in ℝ^n with m, n≥1 and k≥ m are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest degree case k=m, the set of degrees of freedom only involves function values and derivatives up to order m1 at the vertices of the polytope. The inverse inequality and several norm equivalences for the H^mconforming virtual elements are rigorously proved. The H^mconforming virtual elements are then applied to discretize a polyharmonic equation with a lower order term. With the help of the interpolation error estimate and norm equivalences, the optimal error estimates are derived for the H^mconforming virtual element method.
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