A mesh with the minimum possible number of elements that captures all relevant features of the investigated geometry is desired in order to support methods for fast numerical analysis as well as an accurate description of the geometry. This in particular aids the discretization of partial differential equations used for the solution in a reasonable amount of time, computer resources, and minimal manual interaction.
The increase in geometrical feature complexity and number of elements requires a modern software design approach for the actual mesh generation and adaptation codes. Especially regarding the coupling of modeling, mesh generation, and error estimation, mesh adaptation pushes the currently available methods beyond their limits. Programming paradigms with support for orthogonality, reusability, and modularity that still maintain reasonable performance are required. A shift to real three-dimensional devices in the current research can be observed clearly, which obviously requires three-dimensional structure modeling. The three-dimensional mesh generation and adaptation process is therefore becoming essential for successful spatial discretization techniques and any manual interaction for adaptation of the mesh elements by the user can no longer be demanded. Three-dimensional structures lack an intuitive view of user interaction. Therefore assisted or fully automatic mesh generation coupled with error estimation techniques (a-priori and a-posteriori) for the used PDE is required in order to control the mesh adaptation process. Error estimation techniques have shown, that a-priori estimation techniques, such as condition estimations, can be used as a basic guide for the mesh generation, whereas a-posteriori techniques can be used as control instance for adaptation techniques.
The automation and coupling of mesh generation and mesh adaptation driven by control mechanisms, e.g., error estimation (considering the applied partial differential equation's discretization technique and the subsequent properties of the equation system) were investigated.