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Provided with this theoretical backup, and since corresponding Monte-Carlo based realizations are simple to implement, these methods may serve to efficiently approximate solutions of high-dimensional (initial-)boundary value problems.<\/jats:p>","DOI":"10.1007\/s00211-023-01350-2","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T19:02:08Z","timestamp":1682362928000},"page":"827-884","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems"],"prefix":"10.1007","volume":"153","author":[{"given":"Fabian","family":"Merle","sequence":"first","affiliation":[]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"1350_CR1","doi-asserted-by":"crossref","unstructured":"Ali, M., Urban, K.: HT-AWGM: a hierarchical Tucker-adaptive wavelet Galerkin method for high-dimensional elliptic problems, Adv. 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