Abstract.
A key component of domain decomposition solvers for hp discretizations of elliptic equations
is the solver for internal stiffness matrices of p-elements.
We consider an
algorithm which belongs to the family of secondary domain
decomposition solvers, based on the finite-difference like preconditioning of p-elements,
and was outlined by the author earlier. We remove the
uncertainty in the choice of the coarse (decomposition) grid
solver and suggest the new interface Schur complement
preconditioner. The latter essentially uses the boundary norm for discrete harmonic functions
induced by orthotropic discretizations on slim rectangles,
which was derived recently.
We prove that the algorithm has linear arithmetical complexity.