On the Multi-Level Splitting of Finite Element Spaces for Indefinite Elliptic Boundary Value Problems

We continue our work [Bericht 21, Inst. für Geometric and Praktische Mathematik der RWTH Aachen, 1983] concerning the use of hierarchical bases in finite element computations. The present paper deals with indefinite, not necessarily symmetric elliptic boundary value problems. The resulting linear systems are split into two parts, namely into a low-dimensional part, the matrix of which is fixed independent of the number j of refinement levels, and a high-dimensional system, the matrix of which is positive definite and has a condition number growing only quadratically in j.