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• W4226300631 abstract "Abstract We present a low-rank greedily adapted hp -finite element algorithm for computing an approximation to the solution of the Lyapunov operator equation. We show that there is a hidden regularity in eigenfunctions of the solution of the Lyapunov equation which can be utilized to justify the use of high order finite element spaces. Our numerical experiments indicate that we achieve eight figures of accuracy for computing the trace of the solution of the Lyapunov equation posed in a dumbbell-domain using a finite element space of dimension of only $$10^4$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:math> degrees of freedom. Even more surprising is the observation that hp -refinement has an effect of reducing the rank of the approximation of the solution." @default.
• W4226300631 created "2022-05-05" @default.
• W4226300631 creator A5058542887 @default.
• W4226300631 creator A5091633365 @default.
• W4226300631 date "2022-04-07" @default.
• W4226300631 modified "2023-10-14" @default.
• W4226300631 title "High order approximations of the operator Lyapunov equation have low rank" @default.
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• W4226300631 doi "https://doi.org/10.1007/s10543-022-00917-z" @default.
• W4226300631 hasPublicationYear "2022" @default.
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