VERIFIED CALCULATION OF AN ERROR BOUND FOR A SIMPLIFIED ELASTOPLASTICITY MODEL


J ROHE

uafx@rz.uni-karlsruhe.de

Mathematisches Institut I
Universität Karlsruhe
D-76128 Karlsruhe, Germany






We consider a simplified model for nonlinear plasticity. Let $ f \in L^2(\Omega)$,

$\displaystyle S_f = \{ \sigma \in (L_2(\Omega))^2 \vert - \textrm{div} \,\sigma = f \}
$

the equilibrium set, and

$\displaystyle K_f = \{ \sigma \in S_f \vert \ \Vert\sigma\Vert _\infty \le k \},\ k > 0.
$

Then, the convex minimisation problem to be considered is

$\displaystyle \min_{\sigma \in K_f} \Vert \sigma \Vert^2_{(L_2(\Omega))^2}
$

We will propose a method for enclosing the solution $ \sigma$ when $ \Omega$ ist a bounded, simply connected, polygonal domain in $ \mathbf{R}^2$. If $ K_f \neq \emptyset, $ there exists a unique solution. If an approximation for it in $ K_f$ is known, an error bound can be given in the $ L^2$ norm using duality methods. The main difficulty is the construction of an initial element in $ K_f.$



EPSRC Gregynog Workshop, 21-26 July 2002

Gregynog Abstracts