Local error estimates and adaptive refinement for first-order system least squares (FOSLS).
Local error estimates for finite element discretization of the Stokes equations
Local Galerkin and adjoint local Galerkin procedures for elliptic equations
Local refinement techniques for elliptic problems on cell-centered grids. III. Algebraic multilevel BEPS preconditioners.
Locally pointwise superconvergence of the tensor-product finite element in three dimensions
Consider a second-order elliptic boundary value problem in three dimensions with locally smooth coefficients and solution. Discuss local superconvergence estimates for the tensor-product finite element approximation on a regular family of rectangular meshes. It will be shown that, by the estimates for the discrete Green’s function and discrete derivative Green’s function, and the relationship of norms in the finite element space such as -norms, -norms, and negative-norms in locally smooth subsets...
Locking effects in the finite element approximation of elasticity problems.
Locking free matching of different three dimensional models in structural mechanics
The present paper proposes and analyzes a general locking free mixed strategy for computing the deformation of incompressible three dimensional structures placed inside flexible membranes. The model involves as in Chapelle and Ferent [Math. Models Methods Appl. Sci.13 (2003) 573–595] a bending dominated shell envelope and a quasi incompressible elastic body. The present work extends an earlier work of Arnold and Brezzi [Math Comp.66 (1997) 1–14] treating the shell part and proposes a global...
Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity
We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity....