2,823 research outputs found
Stabilized mixed finite element methods for linear elasticity on simplicial grids in
In this paper, we design two classes of stabilized mixed finite element
methods for linear elasticity on simplicial grids. In the first class of
elements, we use - and
- to approximate the stress
and displacement spaces, respectively, for , and employ a
stabilization technique in terms of the jump of the discrete displacement over
the faces of the triangulation under consideration; in the second class of
elements, we use - to
approximate the displacement space for , and adopt the
stabilization technique suggested by Brezzi, Fortin, and Marini. We establish
the discrete inf-sup conditions, and consequently present the a priori error
analysis for them. The main ingredient for the analysis is two special
interpolation operators, which can be constructed using a crucial
bubble function space of polynomials on each
element. The feature of these methods is the low number of global degrees of
freedom in the lowest order case. We present some numerical results to
demonstrate the theoretical estimates.Comment: 16 pages, 1 figur
A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids
A family of stable mixed finite elements for the linear elasticity on
tetrahedral grids are constructed, where the stress is approximated by
symmetric H(\d)- polynomial tensors and the displacement is approximated
by - polynomial vectors, for all . Numerical tests are
provided.Comment: 11. arXiv admin note: substantial text overlap with arXiv:1406.745
Nonconforming tetrahedral mixed finite elements for elasticity
This paper presents a nonconforming finite element approximation of the space
of symmetric tensors with square integrable divergence, on tetrahedral meshes.
Used for stress approximation together with the full space of piecewise linear
vector fields for displacement, this gives a stable mixed finite element method
which is shown to be linearly convergent for both the stress and displacement,
and which is significantly simpler than any stable conforming mixed finite
element method. The method may be viewed as the three-dimensional analogue of a
previously developed element in two dimensions. As in that case, a variant of
the method is proposed as well, in which the displacement approximation is
reduced to piecewise rigid motions and the stress space is reduced accordingly,
but the linear convergence is retained.Comment: 13 pages, 2 figure
Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems
A posteriori error estimators for the symmetric mixed finite element methods
for linear elasticity problems of Dirichlet and mixed boundary conditions are
proposed. Stability and efficiency of the estimators are proved. Finally, we
provide numerical examples to verify the theoretical results
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
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