2 research outputs found
Analysis of a family of HDG methods for second order elliptic problems
In this paper, we analyze a family of hybridizable discontinuous Galerkin
(HDG) methods for second order elliptic problems in two and three dimensions.
The methods use piecewise polynomials of degree for both the
flux and numerical trace, and piecewise polynomials of degree for the
potential. We establish error estimates for the numerical flux and potential
under the minimal regularity condition. Moreover, we construct a local
postprocessing for the flux, which produces a numerical flux with better
conservation. Numerical experiments in two-space dimensions confirm our
theoretical results.Comment: 18 page
Robust weak Galerkin finite element methods for linear elasticity with continuous displacement trace approximation
This paper proposes and analyzes a class of new weak Galerkin (WG) finite
element methods for 2- and 3-dimensional linear elasticity problems. The
methods use discontinuous piecewise-polynomial approximations of degrees
for the stress, for the displacement, and a continuous
piecewise-polynomial approximation of degree for the displacement trace
on the inter-element boundaries, respectively. After the local elimination of
unknowns defined in the interior of elements, the WG methods result in SPD
systems where the unknowns are only the degrees of freedom describing the
continuous trace approximation. We show that the proposed methods are robust in
the sense that the derived a priori error estimates are optimal and uniform
with respect to the Lam\'{e} constant . Numerical experiments confirm
the theoretical results