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

Technical Report · Fri Jul 13 00:00:00 EDT 2012

DOI:https://doi.org/10.2172/1046508· OSTI ID:1046508

Manzini, Gianmarco ^[1]

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1. Los Alamos National Laboratory

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: DOE/LANL
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 1046508
• Report Number(s): LA-UR-12-22977; TRN: US201215%%642
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONVERGENCE
DEGREES OF FREEDOM
DIFFUSION
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD