%AManzini, Gianmarco[Los Alamos National Laboratory]
%B
%D2012%K97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; DEGREES OF FREEDOM; DIFFUSION; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD
%MOSTI ID: 1046508
%PMedium: ED
%TThe Mimetic Finite Element Method and the Virtual Element Method for elliptic problems with arbitrary regularity.
%Uhttp://www.osti.gov/scitech//servlets/purl/1046508/
%XWe develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.
%0Technical Report
%@LA-UR-12-22977; TRN: US201215%%642
United States10.2172/1046508TRN: US201215%%642Wed Dec 05 12:08:30 EST 2012LANLEnglish