| In this dissertation, a number of applications of mesh adaptation techniques are considered.; By means of adaptive grids the fictitious space technique is extended on an arbitrary shape-regular mesh. This allows the construction of efficient preconditioners for stiffness matrices generated by finite element methods on completely unstructured meshes. By introducing a fictitious hierarchical grid adapted to the original triangulation, one obtains a natural infrastructure for a generic multilevel method.; An integrated technique for electrostatic field simulation that utilizes grids, which are locally refined and fitted to the domain boundaries, and solvers based on domain decomposition methods is presented. This approach provides accurate approximations of the problem with a limited number of degrees of freedom and, at the same time, allows the employment of efficient solvers.; The rezoning strategy for Arbitrary Lagrangian-Eulerian methods in CFD gives another example of the adaptive technique for computational meshes. The numerical validation of the Reference Jacobian rezoning algorithm proves the efficiency of this approach for a wide class of domain partitionings including tetrahedral, prismatic, hexahedral and Voronoi meshes. |
