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

Manzini, Gianmarco¹ 

[1]Los Alamos National Laboratory

关键词: CONVERGENCE;    DEGREES OF FREEDOM;    DIFFUSION;    FINITE DIFFERENCE METHOD;    FINITE ELEMENT METHOD;   

DOI  :  10.2172/1046508
RP-ID  :  LA-UR-12-22977
PID  :  OSTI ID: 1046508
Others  :  TRN: US201215%%642

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

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.