{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ACUCZIHIPO2FNBB7MQBJP5MW7O","short_pith_number":"pith:ACUCZIHI","schema_version":"1.0","canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","source":{"kind":"arxiv","id":"2606.04488","version":1},"attestation_state":"computed","paper":{"title":"Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\\bf L}^{2}$-norm error estimates","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Achyuta Ranjan Dutta Mohapatra, Bhupen Deka","submitted_at":"2026-06-03T06:13:50Z","abstract_excerpt":"We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \\( {\\bf L}^{2} \\) norms for the electric field variable, as well as in \\( L^{2} \\) norm for the potential function. To the best of our knowledge, this work provides the first optimal \\( {\\bf L}^{2} \\)-norm error analysis for the second-order time-dependent saddle point Maxwell equations using any variants of FEMs. Addi"},"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":"2606.04488","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T06:13:50Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0efd353b1ce66c28296aba7460251a1d00cfba1ad5892959745f24b1aa50be93","abstract_canon_sha256":"469b3fb27df3867500e37c980fce8111af634c26e2bac46ea538889e90cc5345"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:10.267199Z","signature_b64":"c6iVwtV2HNEM/YN9NCxiaK9+0E2rkqDGbR0mj48Pg0t6SKrt0G7qNlU56tesdW22bK/rDYvnZfVLK5JbcJKoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","last_reissued_at":"2026-06-04T01:09:10.266454Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:10.266454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\\bf L}^{2}$-norm error estimates","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Achyuta Ranjan Dutta Mohapatra, Bhupen Deka","submitted_at":"2026-06-03T06:13:50Z","abstract_excerpt":"We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \\( {\\bf L}^{2} \\) norms for the electric field variable, as well as in \\( L^{2} \\) norm for the potential function. To the best of our knowledge, this work provides the first optimal \\( {\\bf L}^{2} \\)-norm error analysis for the second-order time-dependent saddle point Maxwell equations using any variants of FEMs. Addi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04488","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04488/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.04488","created_at":"2026-06-04T01:09:10.266571+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04488v1","created_at":"2026-06-04T01:09:10.266571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04488","created_at":"2026-06-04T01:09:10.266571+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACUCZIHIPO2F","created_at":"2026-06-04T01:09:10.266571+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACUCZIHIPO2FNBB7","created_at":"2026-06-04T01:09:10.266571+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACUCZIHI","created_at":"2026-06-04T01:09:10.266571+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/ACUCZIHIPO2FNBB7MQBJP5MW7O","json":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O.json","graph_json":"https://pith.science/api/pith-number/ACUCZIHIPO2FNBB7MQBJP5MW7O/graph.json","events_json":"https://pith.science/api/pith-number/ACUCZIHIPO2FNBB7MQBJP5MW7O/events.json","paper":"https://pith.science/paper/ACUCZIHI"},"agent_actions":{"view_html":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O","download_json":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O.json","view_paper":"https://pith.science/paper/ACUCZIHI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04488&json=true","fetch_graph":"https://pith.science/api/pith-number/ACUCZIHIPO2FNBB7MQBJP5MW7O/graph.json","fetch_events":"https://pith.science/api/pith-number/ACUCZIHIPO2FNBB7MQBJP5MW7O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/action/storage_attestation","attest_author":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/action/author_attestation","sign_citation":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/action/citation_signature","submit_replication":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/action/replication_record"}},"created_at":"2026-06-04T01:09:10.266571+00:00","updated_at":"2026-06-04T01:09:10.266571+00:00"}