2022/05/18 by Carsten Carstensen, Carstensen, Carsten, Rekha Khot +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2205.08764
openalex publication_date 2022/05/18 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28
The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution u∈ V:=H20(Ω) 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-2(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:Vh→ 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.