9 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
Robust globally divergence-free weak Galerkin finite element methods for natural convection problems
This paper proposes and analyzes a class of weak Galerkin (WG) finite element
methods for stationary natural convection problems in two and three dimensions.
We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity,
pressure, and temperature approximations in the interior of elements,
respectively, and piecewise polynomials of degrees l, k, l(l = k-1,k) for the
numerical traces of velocity, pressure and temperature on the interfaces of
elements. The methods yield globally divergence-free velocity solutions.
Well-posedness of the discrete scheme is established, optimal a priori error
estimates are derived, and an unconditionally convergent iteration algorithm is
presented. Numerical experiments confirm the theoretical results and show the
robustness of the methods with respect to Rayleigh number.Comment: 32 pages, 13 figure