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We provide a rigorous stability and convergence analysis of a fully discrete L1-ADI scheme for solving the multi-term time fractional diffusion problem. Numerical results show that the error estimate is sharp.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023064","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T12:21:27Z","timestamp":1688041287000},"page":"1454-1470","source":"Crossref","is-referenced-by-count":12,"title":["Error estimate of L1-ADI scheme for two-dimensional multi-term time fractional diffusion equation"],"prefix":"10.3934","volume":"18","author":[{"given":"Kexin","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hu","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shusen","family":"Xie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023064-1","doi-asserted-by":"publisher","unstructured":"D. Cao, H. 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