Preconditioning high order \(H^2\) conforming finite elements on triangles
The authors are concerned with the p-version of FEM approximation of some fourth order linear elliptic problems on regular triangulations. As the condition number of the stiffness matrix typically grows rapidly with the polynomial degree p and the numbers of elements, the authors develop a preconditioner which ameliorates this bleak situation. The preconditioner is based on a smart decomposition of the global finite element space into local subspaces augmented with a global lower order vertex space. The analysis of the preconditioner on a single triangular element and the implementation aspects, including the construction of the vertex basis functions, is thoroughly performed. Three classical problems, namely ; Airy stress tensor, Stokes in a cavity domain with parabolic inflow and outflow velocity profiles and the plate one on a L-shaped domain with point loading are solved in order to underline the performances of the preconditioning technique.
scientific article; zbMATH DE number 7368938
scientific article