@article{Szymczak_Paszyński_Pardo_Paszyńska_2015, title={Petri Nets Modeling of Dead-End Refinement Problems in a 3D Anisotropic hp-Adaptive Finite Element Method}, volume={34}, url={https://www.cai.sk/ojs/index.php/cai/article/view/1839}, abstractNote={We consider two graph grammar based Petri nets models for anisotropic refinements of three dimensional hexahedral grids. The first one detects possible dead-end problems during the graph grammar based anisotropic refinements of the mesh. The second one employs an enhanced graph grammar model that is actually dead-end free. We apply the resulting algorithm to the simulation of resistivity logging measurements for estimating the location of underground oil and/or gas formations. The graph grammar based Petri net models allow to fix the self-adaptive mesh refinement algorithm and finish the adaptive computations with the required accuracy needed by the numerical solution.}, number={2}, journal={COMPUTING AND INFORMATICS}, author={Szymczak, Arkadiusz and Paszyński, Maciej and Pardo, David and Paszyńska, Anna}, year={2015}, month={Oct.}, pages={425–457} }