From the viewpoint of the adaptive solution of partial differential equations a finit e element method on hierarchical triangular meshes is developed permitting hanging nodes arising from nonuniform hierarchical refinement. Construction, extension and restriction of the nonuniform hierarchical basis and the accompanying mesh are described by graphs. The corresponding FE basis is generated by hierarchical transformation. The characteristic feature of the generalizable concept is the combination of the conforming hierarchical basis for easily defining and changing the FE space with an accompanying nonconforming FE basis for the easy assembly of a FE equations system. For an elliptic model the conforming FEM problem is solved by an iterative method applied to this nonconforming FEM equations system and modified by projection into the subspace of conforming basis functions. The iterative method used is the Yserentant- or BPX-preconditioned conjugate gradient algorithm. On a MIMD computer system the parallelization by domain decomposition is easy and efficient to organize both for the generation and solution of the equations system and for the change of basis and mesh.

From the viewpoint of the adaptive solution of partial differential equations a finit e element method on hierarchical triangular meshes is developed permitting hanging nodes arising from nonuniform hierarchical refinement. Construction, extension and restriction of the nonuniform hierarchical basis and the accompanying mesh are described by graphs. The corresponding FE basis is generated by hierarchical transformation. The characteristic feature of the generalizable concept is the combination of the conforming hierarchical basis for easily defining and changing the FE space with an accompanying nonconforming FE basis for the easy assembly of a FE equations system. For an elliptic model the conforming FEM problem is solved by an iterative method applied to this nonconforming FEM equations system and modified by projection into the subspace of conforming basis functions. The iterative method used is the Yserentant- or BPX-preconditioned conjugate gradient algorithm. On a MIMD computer system the parallelization by domain decomposition is easy and efficient to organize both for the generation and solution of the equations system and for the change of basis and mesh.