We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.
|Number of pages||18|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - May 2011|
- finite element
- computable error bounds
Ainsworth, M., & Rankin, R. A. R. (2011). Realistic computable error bounds for three dimensional finite element analyses in linear elasticity. Computer Methods in Applied Mechanics and Engineering, 200(21-22), 1909-1926. https://doi.org/10.1016/j.cma.2011.01.017