In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we are able to propose a variant of the scheme that allows one to take advantage of polygons with many edges (such as those composing Voronoi meshes or generated by agglomeration procedures) in order to yield a more accurate discrete solution. The theoretical results are supported by numerical experiments.
Beirao da Veiga, L., Vacca, G. (2022). Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version. SIAM JOURNAL ON NUMERICAL ANALYSIS, 60(4), 1853-1878 [10.1137/21M1411275].
Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version
Beirao da Veiga, LPrimo
;
2022
Abstract
In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we are able to propose a variant of the scheme that allows one to take advantage of polygons with many edges (such as those composing Voronoi meshes or generated by agglomeration procedures) in order to yield a more accurate discrete solution. The theoretical results are supported by numerical experiments.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.