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Particular examples\nare image processing and phase field models in which jumps across lower\ndimensional subsets and sharp transitions across interfaces are of\ninterest. The numerical solution of corresponding model problems via\na spectral method is analyzed. Its efficiency\nand features of the model problems are illustrated by numerical experiments.<\/jats:p>","DOI":"10.1515\/cmam-2017-0039","type":"journal-article","created":{"date-parts":[[2017,9,3]],"date-time":"2017-09-03T10:02:33Z","timestamp":1504432953000},"page":"661-678","source":"Crossref","is-referenced-by-count":59,"title":["Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling"],"prefix":"10.1515","volume":"17","author":[{"given":"Harbir","family":"Antil","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences , George Mason University , Fairfax , VA 22030 , USA"}]},{"given":"S\u00f6ren","family":"Bartels","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Mathematical Institut e, University of Freiburg , Hermann-Herder-Str. 9, 79104 Freiburg im Breisgau , Germany"}]}],"member":"374","published-online":{"date-parts":[[2017,9,3]]},"reference":[{"key":"2023033116270857767_j_cmam-2017-0039_ref_001_w2aab3b7b9b1b6b1ab1b7b1Aa","doi-asserted-by":"crossref","unstructured":"M.  Ainsworth and Z.  Mao,\nAnalysis and Approximation of a fractional Cahn\u2013Hilliard equation,\nSIAM J. Numer. Anal. 55 (2017), no. 4, 1689\u20131718.\n10.1137\/16M1075302","DOI":"10.1137\/16M1075302"},{"key":"2023033116270857767_j_cmam-2017-0039_ref_002_w2aab3b7b9b1b6b1ab1b7b2Aa","unstructured":"H.  Antil, J.  Pfefferer and S.  Rogovs,\nFractional operators with inhomogeneous boundary conditions: Analysis, control, and discretization,\npreprint (2017), https:\/\/arxiv.org\/abs\/1703.05256."},{"key":"2023033116270857767_j_cmam-2017-0039_ref_003_w2aab3b7b9b1b6b1ab1b7b3Aa","doi-asserted-by":"crossref","unstructured":"H.  Antil, J.  Pfefferer and M.  Warma,\nA note on semilinear fractional elliptic equation: Analysis and discretization,\nESAIM Math. Model. Numer. Anal. (2017), 10.1051\/m2an\/2017023.","DOI":"10.1051\/m2an\/2017023"},{"key":"2023033116270857767_j_cmam-2017-0039_ref_004_w2aab3b7b9b1b6b1ab1b7b4Aa","doi-asserted-by":"crossref","unstructured":"U.  A\u00dfmann and A.  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