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- W4280533535 abstract "The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution $uin V:=H^2_0(Omega)$ to the biharmonic equation. The abstract framework allows (even a mixture of) two examples of the local discrete spaces $V_h(P)$ and a smoother allows rough source terms $Fin V^*=H^{-2}(Omega)$. The a priori and a posteriori error analysis in this paper circumvents any trace of second derivatives by some computable conforming companion operator $J:V_hto V$ from the nonconforming virtual element space $V_h$. 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 $uin V$. 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." @default.
- W4280533535 created "2022-05-22" @default.
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- W4280533535 date "2022-05-18" @default.
- W4280533535 modified "2023-09-28" @default.
- W4280533535 title "Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes" @default.
- W4280533535 doi "https://doi.org/10.48550/arxiv.2205.08764" @default.
- W4280533535 hasPublicationYear "2022" @default.
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