2021/01/21 by Carsten Carstensen, Carstensen, Carsten, Rekha Khot +3
Engineering · #65N12 #65N15 #65N30 #65N50 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2101.08472
openalex publication_date 2021/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The main tool in the a priori error analysis is the connection between the nonconforming virtual element space and the Sobolev space H10(Ω) by a right-inverse J of the interpolation operator Ih. The stability of the discrete solution allows for the proof of existence of a unique discrete solution, of a discrete inf-sup estimate and, consequently, for optimal error estimates in the H1 and L2 norms. The explicit residual-based a posteriori error estimate for the NCVEM is reliable and efficient up to the stabilization and oscillation terms. Numerical experiments on different types of polygonal meshes illustrate the robustness of an error estimator and support the improved convergence rate of an adaptive mesh-refinement in comparison to the uniform mesh-refinement.