Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

On Locking-free Finite Element Schemes for Three-dimensional Elasticity

In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lamé constant λ → ∞. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to λ ∈ (0, +∞) are obtained for t...

Rigorous error bounds for finite dimensional linear programming problems

Finite Element Methods for Linear Elasticity

Conditions for Stable Approximation Schemes Basic idea: Mimic structure of continuous problem. To establish stability of continuous problem, only used last two spaces in top sequence and last three spaces in bottom sequence. Λn−1(K) dn−1 −−−→ Λn(K)→ 0 ↗ Sn−2 ↗ Sn−1 Λn−2(V) dn−2 −−−→ Λn−1(V) dn−1 −−−→ Λn(V)→ 0. Thus, look for five finite dimensional spaces connected by a similar structure, i.e.,...

Computable backward error bounds for basic algorithms in linear algebra

Standard error estimates in numerical linear algebra are often of the form γk|R||S| where R,S are known matrices and γk := ku/(1−u) with u denoting the relative rounding error unit. Recently we showed that for a number of standard problems γk can be replaced by ku for any order of computation and without restriction on the dimension. Such problems include LUand Cholesky decomposition, triangula...

Computable Error Bounds for Finite Element Approximation on Non-polygonal Domains

Fully computable, guaranteed bounds are obtained on the error in the finite element approximation which take the effect of the boundary approximation into account. We consider the case of piecewise affine approximation of the Poisson problem with pure Neumann boundary data, and obtain a fully computable quantity which is shown to provide a guaranteed upper bound on the energy norm of the error....