New results on adaptive virtual element methods
Please login to view abstract download link
A standard Adaptive Finite Element Method for self-adjoint coercive problems is realized by preserving the mesh conformity, which implies the refinement of some elements just for geometric reasons and not marked for their contribution to the global error estimator. The Virtual Element Method (VEM) opens a new perspective in this field, allowing the presence of elements with hanging nodes. This point of view is at the basis of the recent paper [L. Beirão da Veiga et al. , 2023] devoted to the convergence analysis of an adaptive VEM in the lowest-order case built on triangular meshes. This talk discusses how to extend these results to the case of VEMs of order k ≥ 2 built on triangular and on tetrahedral meshes. In particular we derive a stabilization-free a posteriori error estimator and we prove the convergence of an adaptive VEM based on this estimator.
