Hm-CONFORMING VIRTUAL ELEMENTS IN ARBITRARY DIMENSION

Authors：Chen, Chunyu; Huang, Xuehai^*; Wei, Huayi

Source：SIAM Journal on Numerical Analysis, 2022, 60(6): 3099-3123.

DOI：10.1137/21M1440323

• H m -conforming virtual elements
• Whitney array
• error analysis
• polyharmonic

The Hm-conforming virtual elements of any degree k on any shape of polytope in Rn with m, n \geq 1 and k \geq 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 m -1 at the vertices of the polytope. The inverse inequality and several norm equivalences for the Hm-conforming virtual elements are rigorously proved. The Hm-conforming 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 Hm-conforming virtual element method.

• Institution
  湘潭大学