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The refinement algorithm

As mentioned above the initial triangulation must not include elements with obtuse faces in order to preserve stability. If an appropriate finite element mesh is created, the finite element calculations can be performed to produce the desired results and select certain elements for regular refinement. All selected regular or regularly refined elements are refined as described above. Irregular elements must not be refined because this could lead to degenerated elements and disturb the calculations' stability. As a consequence irregular elements and their ``brothers'', who belong to the same father, are removed and their father is refined regularly.

After performing this first refinement called the red closure, the triangulation is closed with irregular elements (green closure). If none of the four irregular refinement patterns is applicable for a certain element, it is refined regularly and its neighbouring elements are new candidates for the green closure.

This procedure is applied until all selected elements are refined and the whole grid is closed properly.

Werner Scholz