{"paper":{"title":"A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"B. Abdallah, K.M. Furati, K. Mustapha, M. Nour","submitted_at":"2015-10-31T19:16:57Z","abstract_excerpt":"We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order $\\mu\\in (0,1)$ with variable coefficients. For the spatial discretization, we apply the standard piecewise linear continuous Galerkin method. Well-posedness of the fully discrete scheme and error analysis will be shown. For a time interval~$(0,T)$ and a spatial domain~$\\Omega$, our analysis suggest that the error in $L^2\\bigr((0,T),L^2(\\Omega)\\bigr)$-norm is of order $O(k^{2-\\frac{\\mu}{2}}+h^2)$ (that is, short by order $\\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00163","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}