A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
On locking and robustness in the finite element method
SIAM Journal on Numerical Analysis
Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
SIAM Journal on Numerical Analysis
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
SIAM Journal on Scientific Computing
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
| Hi-index | 0.00 |
A compact discontinuous Galerkin method (CDG) is devised for nearly incompressible linear elasticity, through replacing the global lifting operator for determining the numerical trace of stress tensor in a local discontinuous Galerkin method (cf. Chen et al., Math Probl Eng 20, 2010) by the local lifting operator and removing some jumping terms. It possesses the compact stencil, that means the degrees of freedom in one element are only connected to those in the immediate neighboring elements. Optimal error estimates in broken energy norm, $$H^1$$ -norm and $$L^2$$ -norm are derived for the method, which are uniform with respect to the Lamé constant $$\lambda .$$ Furthermore, we obtain a post-processed $$H(\text{ div})$$ -conforming displacement by projecting the displacement and corresponding trace of the CDG method into the Raviart---Thomas element space, and obtain optimal error estimates of this numerical solution in $$H(\text{ div})$$ -seminorm and $$L^2$$ -norm, which are uniform with respect to $$\lambda .$$ A series of numerical results are offered to illustrate the numerical performance of our method.