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The approximate solution will be sought as a continuous piecewise linear function in time <jats:italic>t<\/jats:italic> and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(\\tau ^{1+ \\alpha }), \\, \\alpha \\in (0, 1)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:msup>\n                        <mml:mi>\u03c4<\/mml:mi>\n                        <mml:mrow>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mo>+<\/mml:mo>\n                          <mml:mi>\u03b1<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:msup>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mspace\/>\n                    <mml:mi>\u03b1<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mn>0<\/mml:mn>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mn>1<\/mml:mn>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\tau $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c4<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich\u2019s convolution methods) and L-type methods (e.g., L1 method), which have only <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(\\tau )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>\u03c4<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity.\n<\/jats:p>","DOI":"10.1007\/s10915-021-01587-9","type":"journal-article","created":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T10:03:40Z","timestamp":1627553020000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Error Estimates of a Continuous Galerkin Time Stepping Method for Subdiffusion Problem"],"prefix":"10.1007","volume":"88","author":[{"given":"Yuyuan","family":"Yan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernard A.","family":"Egwu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongqi","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5686-5017","authenticated-orcid":false,"given":"Yubin","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,7,29]]},"reference":[{"key":"1587_CR1","doi-asserted-by":"publisher","first-page":"3293","DOI":"10.1029\/92WR01757","volume":"28","author":"EE Adams","year":"1992","unstructured":"Adams, E.E., Gelhar, L.W.: Field study of dispersion in a heterogeneous aquifer: $$2$$. 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