Least-Squares Spectral Element Methods in Computational Fluid Dynamics

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.

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Model based on population balance for the simulation of bubble columns using methods of the least-square type

Sporleder¹,

Dorao²,

Jakobsen³

2011

Chemical Engineering Science

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Least-Squares Spectral Element Methods in Computational Fluid Dynamics

Cited by 7 publications

References 60 publications

Exponentially Accurate Spectral Element Method for Fourth Order Elliptic Problems

Exponentially Accurate Spectral Element Method for Fourth Order Elliptic Problems

Least-squares spectral element preconditioners for fourth order elliptic problems

Model based on population balance for the simulation of bubble columns using methods of the least-square type

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