Sharper Error Estimates for Virtual Elements and a Bubble-Enriched Version
L. Beirão da Veiga, Giuseppe Vacca
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.
Topics & Concepts
Polygon meshVoronoi diagramMathematicsBubbleElement (criminal law)Boundary (topology)Finite element methodApplied mathematicsAlgorithmMathematical optimizationGeometryMathematical analysisComputer sciencePolitical scienceParallel computingThermodynamicsPhysicsLawAdvanced Numerical Methods in Computational MathematicsNumerical methods in engineeringComputational Fluid Dynamics and Aerodynamics