A posteriori error estimation for an interior penalty virtual element method of Kirchhoff plates (2406.11411v2)

Abstract: A residual-type a posteriori error estimation is developed for an interior penalty virtual element method (IPVEM) to solve a Kirchhoff plate bending problem with inhomogeneous boundary value conditions. The computable error estimator is incorporated. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates that align with interior penalty finite element methods. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results on several benchmark tests confirm the robustness of the proposed error estimator and show the efficiency of the resulting adaptive VEM.