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The Morley-Type Virtual Element for Plate Bending Problems
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Journal Article
The Morley-Type Virtual Element for Plate Bending Problems
2018
Overview
We propose a simple nonconforming virtual element for plate bending problems, which has few local degrees of freedom and provides the optimal convergence in
H
2
-norm. Moreover, we prove the optimal error estimates in
H
1
- and
L
2
-norm. The nonconforming virtual element is constructed for any order of accuracy, but not
C
0
-continuous. It is worth mentioning that, for the lowest-order case on triangular meshes the simplified nonconforming virtual element coincides with the well-known Morley element, so it can be taken as the extension of the Morley element to polygonal meshes. Finally, we verify the optimal convergence in
H
2
-norm for the nonconforming virtual element by some numerical tests.
Publisher
Springer US,Springer Nature B.V
