720 research outputs found
Virtual Enriching Operators
We construct bounded linear operators that map conforming Lagrange
finite element spaces to conforming virtual element spaces in two and
three dimensions. These operators are useful for the analysis of nonstandard
finite element methods
Virtual Element Methods on Meshes with Small Edges or Faces
We consider a model Poisson problem in () and establish error
estimates for virtual element methods on polygonal or polyhedral meshes that
can contain small edges () or small faces ().Comment: 36 page
A Robust Solver for a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation
We develop a robust solver for a second order mixed finite element splitting
scheme for the Cahn-Hilliard equation. This work is an extension of our
previous work in which we developed a robust solver for a first order mixed
finite element splitting scheme for the Cahn-Hilliard equaion. The key
ingredient of the solver is a preconditioned minimal residual algorithm (with a
multigrid preconditioner) whose performance is independent of the spacial mesh
size and the time step size for a given interfacial width parameter. The
dependence on the interfacial width parameter is also mild.Comment: 17 pages, 3 figures, 4 tables. arXiv admin note: substantial text
overlap with arXiv:1709.0400
A quadratic nonconforming vector finite element for H (curl ; Ω) ∩ H (div ; Ω)
We present a quadratic nonconforming vector finite element for problems posed on the space H (curl ; Ω) ∩ H (div ; Ω), where Ω ⊂ R . Generalizations to higher order and higher dimension are also discussed. © 2008 Elsevier Ltd. All rights reserved.
Balancing domain decomposition for nonconforming plate elements
In this paper the balancing domain decomposition method is extended to nonconforming plate elements. The condition number of the preconditioned system is shown to be bounded by C[1 + ln(H/h)] , where H measures the diameters of the subdomains, h is the mesh size of the triangulation, and the constant C is independent of H, h and the number of subdomains.
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