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The proposed approach yields a drastic reduction of the computational complexity in terms of degrees of freedom and even has slightly improved convergence properties compared to the state-of-the-art discretization using linear finite elements for both the original domain and the extended direction. The performance of the method is illustrated by numerical experiments.<\/jats:p>","DOI":"10.1137\/17m1135517","type":"journal-article","created":{"date-parts":[[2018,8,2]],"date-time":"2018-08-02T13:26:52Z","timestamp":1533216412000},"page":"2345-2374","source":"Crossref","is-referenced-by-count":26,"title":["$hp$-Finite Elements for Fractional Diffusion"],"prefix":"10.1137","volume":"56","author":[{"given":"Dominik","family":"Meidner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Pfefferer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Klemens","family":"Sch\u00fcrholz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boris","family":"Vexler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"atypb1","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz M."},{"key":"atypb2","volume-title":"Finite Element Approximations for Fractional Evolution Problems, arXiv:1705.09815","author":"Acosta G.","year":"2017"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2017.05.026"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/15M1033952"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3276"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1476(19960110)19:1<63::AID-MMA764>3.0.CO;2-S"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2016.10.016"},{"key":"atypb8","volume-title":"Numerical Approximation of Space-Time Fractional Parabolic Equations, arXiv:1704.04254","author":"Bonito A.","year":"2017"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2015-02937-8"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drw067"},{"key":"atypb11","volume-title":"Finite Element Approximation for the Fractional Eigenvalue Problem, arXiv:1603.00317","author":"Borthagaray J. 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