Experiments in 3D with a three-point hierarchical basis preconditioner Original Research Article

A recently introduced hierarchical basis preconditioner is applied to three-dimensional symmetric elliptic boundary value problems discretized on linear finite element spaces. Each hierarchical basis function is a linear combination of three nodal basis functions on its level. The preconditioner turns out to be robust for non-negative linear combinations of second and zeroth order elliptic differential operators, for differential operators with discontinuous coefficients and for anisotropic problems.