Isotropic volume and surface mesh adaptation driven by a Zienkiewicz-Zhu error estimator with an application to haemodynamics

Zonca, Stefano

Isotropic volume and surface mesh adaptation driven by a Zienkiewicz-Zhu error estimator with an application to haemodynamics

Thursday 3rd October 2013

Perotto, S.

Faggiano, E.

This thesis deals with methods for generating isotropic meshes to effectively describe the solution of PDE problems. This goal is pursued by properly adapting the mesh in accordance with the geometry of the considered computational domain or the employment of an a posteriori error estimator, i.e., the one proposed in 1987 by O.C. Zienkiewicz and J.Z. Zhu. These two approaches allow us to generate meshes that better fit the features of the problem at hand while leading at the same time to a reduction of the computational costs. The adaptive procedure we employ is based on the use of a suitable size-function, which essentially tunes the size of the mesh elements. Some test cases are studied to validate the procedure. Moreover, an interesting application to haemodynamics is considered to assess the proposed technique on a more challenging configuration. The results show that the adapted meshes may significantly affect the quality of the numerical approximation. This confirms the benefits given by the employment of ad-hoc adapted meshes, able to follow the phenomenon under investigation.