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NONCONFORMING VIRTUAL ELEMENTS FOR THE BIHARMONIC EQUATION WITH MORLEY DEGREES OF FREEDOM ON POLYGONAL MESHES.
- Source :
- SIAM Journal on Numerical Analysis; 2023, Vol. 61 Issue 5, p2460-2484, 25p
- Publication Year :
- 2023
-
Abstract
- The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution u ∊ V := H2 0 (\Omega) to the biharmonic equation. The abstract framework allows (even a mixture of) two examples of the local discrete spaces Vh(P) and a smoother allows rough source terms F ∊ V* =H<superscript>-2</superscript><subscript>0</subscript>(Ω). The a priori and a posteriori error analysis in this paper circumvents any trace of second derivatives by some computable conforming companion operator J: V<subscript>h</subscript> → V from the nonconforming virtual element space Vh. The operator J is a right-inverse of the interpolation operator and leads to optimal error estimates in piecewise Sobolev norms without any additional regularity assumptions on u ∊ V. As a smoother the companion operator modifies the discrete right-hand side and then allows a quasi-best approximation. An explicit residual-based a posteriori error estimator is reliable and efficient up to data oscillations. Numerical examples display the predicted empirical convergence rates for uniform and optimal convergence rates for adaptive mesh-refinement. [ABSTRACT FROM AUTHOR]
- Subjects :
- A posteriori error analysis
BIHARMONIC equations
DEGREES of freedom
Subjects
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 61
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 173599880
- Full Text :
- https://doi.org/10.1137/22M1496761