TBA
Tuesday, 16.1.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
TBA
The p-Laplacien in the setting of multi-valued operators.
Tuesday, 16.1.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
\nAbstract: The thesis provides proofs for the existence of solutions for both the stationary problem\n\[ \blambda u + Au \bni f \bin \bOmega \bsubset R^N;~~ u=0 ~\btext{on}~~ \bpartial \bOmega\] \nand the non-stationary problem \n\[dy(t)/dt + Ay(t) \bni f(t) ~ \btext{for}~ t\bin[0,T];~~ y(0)=y_0 \]for A being a maximal monotone/accretive operator on \(L^2(\bOmega)\). It especially considers such operators A that arise as the sub-differential of some energy-functional and also shows some regularity for them in the non-stationary case. As an example the theory is applied to the p-Laplace operator.\n
A-priori bounds for geometric FE discretizations of a Cosserat rod and simulations for microheterogeneous prestressed rods
Tuesday, 23.1.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In summary, this thesis focuses on developing an a priori theory for geometric finite\nelement discretizations of a Cosserat rod model, which is derived from incompatible\nelasticity. This theory will be supported by corresponding numerical experiments\nto validate the convergence behavior of the proposed method.\nThe main result describes the qualitative behavior of intrinsic H 1 -errors and\n\nL^2 -errors in terms of the mesh diameter 0 < h ≪ 1 of the approximation scheme:\n\nD 1,2 (u, u h ) ≲ h m , d L 2 (u, u h ) ≲ h m+1 ,\n\nfor a sequence of m-order discrete solutions u h and an exact solution u.