{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AYICK5S4LT4VEUYE7TV6XMZ5L3","short_pith_number":"pith:AYICK5S4","schema_version":"1.0","canonical_sha256":"061025765c5cf9525304fcebebb33d5ee17ad58e148ac8733a1a6f3ec39cf3a4","source":{"kind":"arxiv","id":"1511.00163","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.00163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-31T19:16:57Z","cross_cats_sorted":[],"title_canon_sha256":"e17d889f095c6e08760ab898fda44b008b3235188a7b5654b0d541009c52bbd7","abstract_canon_sha256":"40145920493e4064c60ef3a32f45ce3a2c8a005cfbb1a302fd7c9d168c2772c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:13.095877Z","signature_b64":"IDJn0/WLPe2FGV5EvIyhB7pUKYT9q1ixRZa3eYyANeBJk+VYTAdORC7Xz6ATNyN3GdxZuN6xtO3OYA9bYwRSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"061025765c5cf9525304fcebebb33d5ee17ad58e148ac8733a1a6f3ec39cf3a4","last_reissued_at":"2026-05-18T01:28:13.095124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:13.095124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.00163","created_at":"2026-05-18T01:28:13.095226+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00163v1","created_at":"2026-05-18T01:28:13.095226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00163","created_at":"2026-05-18T01:28:13.095226+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYICK5S4LT4V","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYICK5S4LT4VEUYE","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYICK5S4","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3","json":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3.json","graph_json":"https://pith.science/api/pith-number/AYICK5S4LT4VEUYE7TV6XMZ5L3/graph.json","events_json":"https://pith.science/api/pith-number/AYICK5S4LT4VEUYE7TV6XMZ5L3/events.json","paper":"https://pith.science/paper/AYICK5S4"},"agent_actions":{"view_html":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3","download_json":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3.json","view_paper":"https://pith.science/paper/AYICK5S4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00163&json=true","fetch_graph":"https://pith.science/api/pith-number/AYICK5S4LT4VEUYE7TV6XMZ5L3/graph.json","fetch_events":"https://pith.science/api/pith-number/AYICK5S4LT4VEUYE7TV6XMZ5L3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3/action/storage_attestation","attest_author":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3/action/author_attestation","sign_citation":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3/action/citation_signature","submit_replication":"https://pith.science/pith/AYICK5S4LT4VEUYE7TV6XMZ5L3/action/replication_record"}},"created_at":"2026-05-18T01:28:13.095226+00:00","updated_at":"2026-05-18T01:28:13.095226+00:00"}