450 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
Lower Bounds in Domain Decomposition
An important indicator of the efficiency of a domain decomposition preconditioner is the condition number of the preconditioned system. Upper bounds for the condition numbers of the preconditioned systems have been the focus of most analyses in domain decomposition [21, 20, 23]. However, in order to have a fair comparison of two preconditioners, the sharpness of the respective upper bounds must first be established, which means that we need to derive lower bounds for the condition numbers of the preconditioned systems
Lower bounds for two-level additive schwarz preconditioners with small overlap
Lower bounds for the condition numbers of the preconditioned systems are obtained for two-level additive Schwarz preconditioners. They show that the known upper bounds for both second order and fourth order problems are sharp in the case of a small overlap
A General Superapproximation Result
A general superapproximation result is derived in this paper which is useful
for the local/interior error analysis of finite element methods
Multigrid methods for parameter dependent problems
Multigrid methods for parameter dependent problems are discussed. The contraction numbers of the algorithms are proved within a unifying framework to be bounded away from one, independent of the parameter and the mesth levels. Examples include the pure displacement and pure traction boundary value problems in planar linear elasticity, the Timoshenko beam problem, and the Reissner-Mindlin plate problem
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
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