%0 Unpublished Work %1 mcbain2021primitive %A McBain, G. D. %D 2021 %K 65f15-numerical-eigenvalues-eigenvectors 65f35-matrix-norms-conditioning-scaling 76e05-parallel-shear-flows 76m10-finite-element-methods-in-fluid-mechanics %T The primitive Orr-Sommerfeld equation and finite elements %U https://easychair.org/conferences/overview?a=27234140 %X We consider solving the Orr–Sommerfeld equation of linear hydrodynamic stability theory by reverting to the linearized Navier–Stokes equation in velocity and pressure. This second order system can be discretized with simple Mini finite elements rather than the Hermite elements required for the classical fourth-order equation. On computing both solutions using scikit-fem, the primitive-Mini approach is revealed as simple, clear, well-conditioned, and very accurate.

@unpublished{mcbain2021primitive, abstract = {We consider solving the Orr–Sommerfeld equation of linear hydrodynamic stability theory by reverting to the linearized Navier–Stokes equation in velocity and pressure. This second order system can be discretized with simple Mini finite elements rather than the Hermite elements required for the classical fourth-order equation. On computing both solutions using scikit-fem, the primitive-Mini approach is revealed as simple, clear, well-conditioned, and very accurate.}, added-at = {2021-09-02T02:26:48.000+0200}, author = {McBain, G. D.}, biburl = {https://www.bibsonomy.org/bibtex/2dae1c84777ae32155d2eae980e9c6d7e/gdmcbain}, eventdate = {13 - 15 Dec 2021}, eventtitle = {The Fifth Australasian Conference on Computational Mechanics}, interhash = {59587dfbcdccf963c0a469e5b12e0d91}, intrahash = {dae1c84777ae32155d2eae980e9c6d7e}, keywords = {65f15-numerical-eigenvalues-eigenvectors 65f35-matrix-norms-conditioning-scaling 76e05-parallel-shear-flows 76m10-finite-element-methods-in-fluid-mechanics}, timestamp = {2021-09-02T02:26:48.000+0200}, title = {The primitive Orr-Sommerfeld equation and finite elements}, url = {https://easychair.org/conferences/overview?a=27234140}, venue = {The University of Western Sydney}, year = 2021 }