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Title: The Mimetic Finite Element Method and the Virtual Element Method for elliptic problems with arbitrary regularity.

The Mimetic Finite Element Method and the Virtual Element Method for elliptic problems with arbitrary regularity. We 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.
Authors:
Publication Date:
OSTI Identifier:1046508
Report Number(s):LA-UR-12-22977
TRN: US201215%%642
DOE Contract Number:AC52-06NA25396
Resource Type:Technical Report
Research Org:Los Alamos National Laboratory (LANL)
Sponsoring Org:DOE/LANL
Country of Publication:United States
Language:English
Subject: 97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; DEGREES OF FREEDOM; DIFFUSION; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD