@misc{WeiserSchielaDeuflhard, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7352}, number = {03-13}, abstract = {The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.}, language = {en} } @article{SchenklMuggenthalerHubigetal.2017, author = {Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Erdmann, Bodo and Weiser, Martin and Zachow, Stefan and Heinrich, Andreas and G{\"u}ttler, Felix Victor and Teichgr{\"a}ber, Ulf and Mall, Gita}, title = {Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis}, series = {International Journal of Legal Medicine}, volume = {131}, journal = {International Journal of Legal Medicine}, number = {3}, doi = {doi:10.1007/s00414-016-1523-0}, pages = {699 -- 712}, year = {2017}, abstract = {Temperature based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex, but allow a higher accuracy of death time estimation as in principle all relevant cooling mechanisms can be taken into account. Here, a complete work flow for finite element based cooling simulation models is presented. The following steps are demonstrated on CT-phantoms: • CT-scan • Segmentation of the CT images for thermodynamically relevant features of individual geometries • Conversion of the segmentation result into a Finite Element (FE) simulation model • Computation of the model cooling curve • Calculation of the cooling time For the first time in FE-based cooling time estimation the steps from the CT image over segmentation to FE model generation are semi-automatically performed. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using different CTphantoms. Some of the CT phantoms thermodynamic material parameters had to be experimentally determined via independent experiments. Moreover the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis.}, language = {en} }