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Model. and Simul. in Eng. Sci."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this work, the space-time MORe DWR (<jats:underline>M<\/jats:underline>odel <jats:underline>O<\/jats:underline>rder <jats:underline>Re<\/jats:underline>duction with <jats:underline>D<\/jats:underline>ual-<jats:underline>W<\/jats:underline>eighted <jats:underline>R<\/jats:underline>esidual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.<\/jats:p>","DOI":"10.1186\/s40323-024-00262-6","type":"journal-article","created":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T16:02:06Z","timestamp":1713456126000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity"],"prefix":"10.1186","volume":"11","author":[{"given":"Hendrik","family":"Fischer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julian","family":"Roth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ludovic","family":"Chamoin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Am\u00e9lie","family":"Fau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mary","family":"Wheeler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1102-6332","authenticated-orcid":false,"given":"Thomas","family":"Wick","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,18]]},"reference":[{"key":"262_CR1","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1680\/geot.1996.46.2.187","volume":"46","author":"YN Abousleiman","year":"1996","unstructured":"Abousleiman YN, Cheng A, Cui L, Detournay E, Roegiers JC. 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