Least-squares spectral element preconditioners for fourth order elliptic problems
For researchers solving fourth-order elliptic problems with spectral element methods, this provides efficient preconditioners that are easy to invert.
The paper proposes preconditioners for linear systems from spectral element discretizations of fourth-order elliptic problems, showing spectral equivalence to the original quadratic forms and validating with numerical results for the biharmonic problem.
The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element methods. These preconditioners are constructed using separation of variables and can be diagonalized and hence easy to invert. For second order elliptic problems this technique has proven to be very successful and performs better than other preconditioners. We show that these preconditioners are spectrally equivalent to the quadratic forms by which we approximate them. Numerical result for the biharmonic problem are presented to validate the theoretical estimates.