Least-Squares spectral element method on a staggered grid

Authors:
Marc Gerritsma;Mick Bouman;Artur Palha
Affiliations:
TU Delft, Delft, The Netherlands;TU Delft, Delft, The Netherlands;TU Delft, Delft, The Netherlands
Venue:
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Year:
2009

Citing 3
Cited 0

A conservative staggered-grid Chebyshev multidomain method for compressible flows

Journal of Computational Physics
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials

Journal of Computational Physics
On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles

SIAM Journal on Numerical Analysis

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Abstract

This paper describes a mimetic spectral element formulation for the Poisson equation on quadrilateral elements Two dual grids are employed to represent the two first order equations The discrete Hodge operator, which connects variables on these two grids, is the derived Hodge operator obtained from the wedge product and the inner-product The gradient operator is not discretized directly, but derived from the symmetry relation between gradient and divergence on dual meshes, as proposed by Hyman et al., [5], thus ensuring a symmetric discrete Laplace operator The resulting scheme is a staggered spectral element scheme, similar to the staggering proposed by Kopriva and Kolias, [6] Different integration schemes are used for the various terms involved This scheme is equivalent to a least-squares formulation which minimizes the difference between the dual velocity representations This generates the discrete Hodge-⋆ operator The discretization error of this schemes equals the interpolation error.