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Comp."],"abstract":"<p>\n                    We investigate a spectral Galerkin method for the two-dimensional fractional diffusion-reaction equations on a disk. We first prove regularity estimates of solutions in the weighted Sobolev space. Then we obtain optimal convergence orders of a spectral Galerkin method for the fractional diffusion-reaction equations in the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and energy norm. We present numerical results to verify the theoretical analysis.\n                  <\/p>","DOI":"10.1090\/mcom\/3645","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T11:25:48Z","timestamp":1616585148000},"page":"2107-2135","source":"Crossref","is-referenced-by-count":16,"title":["Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk"],"prefix":"10.1090","volume":"90","author":[{"given":"Zhaopeng","family":"Hao","sequence":"first","affiliation":[]},{"given":"Huiyuan","family":"Li","sequence":"additional","affiliation":[]},{"given":"Zhimin","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Zhongqiang","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2021,6,17]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1137\/15M1033952","article-title":"A fractional Laplace equation: regularity of solutions and finite element approximations","volume":"55","author":"Acosta, Gabriel","year":"2017","journal-title":"SIAM J. 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