{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:74TR4FEOEPTFHRVDRVBYZX3HWP","short_pith_number":"pith:74TR4FEO","schema_version":"1.0","canonical_sha256":"ff271e148e23e653c6a38d438cdf67b3c61abb997e2fea3b9b2c5e3be0fa8185","source":{"kind":"arxiv","id":"1607.06704","version":1},"attestation_state":"computed","paper":{"title":"An $hp$-Adaptive Newton-Discontinuous-Galerkin Finite Element Approach for Semilinear Elliptic Boundary Value Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Paul Houston, Thomas P. Wihler","submitted_at":"2016-07-22T15:11:01Z","abstract_excerpt":"In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an $hp$-version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust $hp$-version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples."},"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":"1607.06704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-22T15:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"d19379616c02f1a4ecb114bd9994398740b4b8bae317a6b2b6f9e4d8c516b286","abstract_canon_sha256":"d6d413409f3abc6d989970c9a901b50fbd8c72ef97a55920b70801deb84af167"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:39.252967Z","signature_b64":"2RmDyJ0XEw6v/Gv3frl7CeoMN+DWSbUzYrODYf1CEjWRGT/l/BfUVoP8dZYa6VTyJUSi77jkGf1L1wXdDIjpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff271e148e23e653c6a38d438cdf67b3c61abb997e2fea3b9b2c5e3be0fa8185","last_reissued_at":"2026-05-18T01:10:39.252564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:39.252564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An $hp$-Adaptive Newton-Discontinuous-Galerkin Finite Element Approach for Semilinear Elliptic Boundary Value Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Paul Houston, Thomas P. Wihler","submitted_at":"2016-07-22T15:11:01Z","abstract_excerpt":"In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an $hp$-version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust $hp$-version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06704","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":"1607.06704","created_at":"2026-05-18T01:10:39.252632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06704v1","created_at":"2026-05-18T01:10:39.252632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06704","created_at":"2026-05-18T01:10:39.252632+00:00"},{"alias_kind":"pith_short_12","alias_value":"74TR4FEOEPTF","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"74TR4FEOEPTFHRVD","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"74TR4FEO","created_at":"2026-05-18T12:30:04.600751+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/74TR4FEOEPTFHRVDRVBYZX3HWP","json":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP.json","graph_json":"https://pith.science/api/pith-number/74TR4FEOEPTFHRVDRVBYZX3HWP/graph.json","events_json":"https://pith.science/api/pith-number/74TR4FEOEPTFHRVDRVBYZX3HWP/events.json","paper":"https://pith.science/paper/74TR4FEO"},"agent_actions":{"view_html":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP","download_json":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP.json","view_paper":"https://pith.science/paper/74TR4FEO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06704&json=true","fetch_graph":"https://pith.science/api/pith-number/74TR4FEOEPTFHRVDRVBYZX3HWP/graph.json","fetch_events":"https://pith.science/api/pith-number/74TR4FEOEPTFHRVDRVBYZX3HWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP/action/storage_attestation","attest_author":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP/action/author_attestation","sign_citation":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP/action/citation_signature","submit_replication":"https://pith.science/pith/74TR4FEOEPTFHRVDRVBYZX3HWP/action/replication_record"}},"created_at":"2026-05-18T01:10:39.252632+00:00","updated_at":"2026-05-18T01:10:39.252632+00:00"}