next up previous contents
Next: 3.4.1 Moving Boundaries Up: 3. Mesh Generation Previous: 3.3 Control Space

3.4 Local Adaptation

Local adaptation is necessary to achieve accurate solutions with an acceptable effort in terms of simulation time and memory consumption. The local refinement, coarsening, or smoothing steps are performed to enhance purely geometrical quality aspects as discussed in Section 3.1, or are guided by a control function as explained in the last section. In the first case the refined regions concentrate around areas where the local feature size is small. Large elements which resolve small geometrical features are usually badly shaped and require refinement. In the latter case the mesh density is adapted to a stationary solution or dynamically for each timestep of a transient simulation. The regions of refinement have to migrate as the characteristics of the transient solution change over the domain. Essentially, local refining in some regions as well as local coarsening in other regions becomes necessary to avoid meshing the entire domain repeatedly. The here discussed refinement is often referred to as h-refinement which results in a decrease of the stepsize $h$. On the other hand are p-refinement techniques which increase the order of the polynomial form functions of the finite element approximation. Topics and techniques of local mesh adaptation are discussed in the following paragraphs.



Subsections
next up previous contents
Next: 3.4.1 Moving Boundaries Up: 3. Mesh Generation Previous: 3.3 Control Space
Peter Fleischmann
2000-01-20