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Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods

Abstract : We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual formulation of the evolution problem in Hilbert--Bochner spaces. The discrete solution is sought in a linear trial space composed of tensors of discrete functions in space and in time and is characterized as the unique minimizer of a discrete functional where the dual norm of the residual is evaluated in a space semi-discrete test space. The resulting global space-time linear system is solved iteratively by a greedy algorithm. Numerical results are presented to illustrate the performance of the proposed method on test cases including non-selfadjoint and time-dependent differential operators in space. The results are also compared to those obtained using a fully discrete Petrov--Galerkin setting to evaluate the dual residual norm.
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https://hal.archives-ouvertes.fr/hal-01668316
Contributor : Alexandre Ern <>
Submitted on : Wednesday, October 10, 2018 - 3:35:55 PM
Last modification on : Wednesday, November 20, 2019 - 6:04:11 PM

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Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern, Anthony Nouy. Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2019, 53 (2), pp.635-658. ⟨10.1051/m2an/2018073⟩. ⟨hal-01668316v2⟩

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