{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FWVOU7P2G5MSGI6UJ4MCTGBCC7","short_pith_number":"pith:FWVOU7P2","schema_version":"1.0","canonical_sha256":"2daaea7dfa37592323d44f1829982217ec7c6a134d875b74fcdcd0363bfd0795","source":{"kind":"arxiv","id":"1606.00345","version":3},"attestation_state":"computed","paper":{"title":"Finite element convergence analysis for the thermoviscoelastic Joule heating problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Axel M{\\aa}lqvist, Tony Stillfjord","submitted_at":"2016-06-01T16:19:17Z","abstract_excerpt":"We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector, temperature sensor or for very precise positioning. We introduce a full discretization based on standard finite elements in space and a semi-implicit Euler-type method in time. For this method we prove optimal convergence orders, i.e. second-order in space and first-order in time. The theoretical results are verified by several numerical experiments in two and thr"},"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":"1606.00345","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-01T16:19:17Z","cross_cats_sorted":[],"title_canon_sha256":"f42a93a0817da6de4431594ce4e0fbb4b51bb88afe0550e359f1e25986f5001b","abstract_canon_sha256":"b38d48a4a58ec8d09fb70e59c8aaea6b73a67e75ca601c49b1b4cc2d508b97fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:09.166307Z","signature_b64":"aylBOnV4tcAj7HqXmFRqu/aAeKvIyvqJwQJuDb1RzTjN5Qr62q3Z/gFCNJN4c9+ytfO3pI383ypKmueqwI+4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2daaea7dfa37592323d44f1829982217ec7c6a134d875b74fcdcd0363bfd0795","last_reissued_at":"2026-05-18T00:19:09.165784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:09.165784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite element convergence analysis for the thermoviscoelastic Joule heating problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Axel M{\\aa}lqvist, Tony Stillfjord","submitted_at":"2016-06-01T16:19:17Z","abstract_excerpt":"We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector, temperature sensor or for very precise positioning. We introduce a full discretization based on standard finite elements in space and a semi-implicit Euler-type method in time. For this method we prove optimal convergence orders, i.e. second-order in space and first-order in time. The theoretical results are verified by several numerical experiments in two and thr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00345","kind":"arxiv","version":3},"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":"1606.00345","created_at":"2026-05-18T00:19:09.165868+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00345v3","created_at":"2026-05-18T00:19:09.165868+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00345","created_at":"2026-05-18T00:19:09.165868+00:00"},{"alias_kind":"pith_short_12","alias_value":"FWVOU7P2G5MS","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FWVOU7P2G5MSGI6U","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FWVOU7P2","created_at":"2026-05-18T12:30:15.759754+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/FWVOU7P2G5MSGI6UJ4MCTGBCC7","json":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7.json","graph_json":"https://pith.science/api/pith-number/FWVOU7P2G5MSGI6UJ4MCTGBCC7/graph.json","events_json":"https://pith.science/api/pith-number/FWVOU7P2G5MSGI6UJ4MCTGBCC7/events.json","paper":"https://pith.science/paper/FWVOU7P2"},"agent_actions":{"view_html":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7","download_json":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7.json","view_paper":"https://pith.science/paper/FWVOU7P2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00345&json=true","fetch_graph":"https://pith.science/api/pith-number/FWVOU7P2G5MSGI6UJ4MCTGBCC7/graph.json","fetch_events":"https://pith.science/api/pith-number/FWVOU7P2G5MSGI6UJ4MCTGBCC7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7/action/storage_attestation","attest_author":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7/action/author_attestation","sign_citation":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7/action/citation_signature","submit_replication":"https://pith.science/pith/FWVOU7P2G5MSGI6UJ4MCTGBCC7/action/replication_record"}},"created_at":"2026-05-18T00:19:09.165868+00:00","updated_at":"2026-05-18T00:19:09.165868+00:00"}