{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:2JXUKCJTAASZQTJAFMI2PP24QZ","short_pith_number":"pith:2JXUKCJT","canonical_record":{"source":{"id":"2012.03560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-12-07T10:00:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"57c382afe59e89ab271511c3aaf82e74efe8d3db38413b74075fe94de90e8ec0","abstract_canon_sha256":"0d851b989260069faa1880e38290c56f000cfcb855fc859a3d99bcb1fed8f58f"},"schema_version":"1.0"},"canonical_sha256":"d26f4509330025984d202b11a7bf5c8655e5c22ddd5fd30d626c26695fde3a9e","source":{"kind":"arxiv","id":"2012.03560","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03560","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03560v1","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03560","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"2JXUKCJTAASZ","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"pith_short_16","alias_value":"2JXUKCJTAASZQTJA","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"pith_short_8","alias_value":"2JXUKCJT","created_at":"2026-07-05T01:57:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:2JXUKCJTAASZQTJAFMI2PP24QZ","target":"record","payload":{"canonical_record":{"source":{"id":"2012.03560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-12-07T10:00:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"57c382afe59e89ab271511c3aaf82e74efe8d3db38413b74075fe94de90e8ec0","abstract_canon_sha256":"0d851b989260069faa1880e38290c56f000cfcb855fc859a3d99bcb1fed8f58f"},"schema_version":"1.0"},"canonical_sha256":"d26f4509330025984d202b11a7bf5c8655e5c22ddd5fd30d626c26695fde3a9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:31.113801Z","signature_b64":"mzHe5akgUINLzD3BuNdxM7ObwfgwMKU2YSOup3h52OU9WI6lvdyf+XJt1euDzI/KRKNECg084/MUqsEziKpXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d26f4509330025984d202b11a7bf5c8655e5c22ddd5fd30d626c26695fde3a9e","last_reissued_at":"2026-07-05T01:57:31.113408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:31.113408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.03560","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ieQcSDA2JDYr/4mboPXOpBvEzgyPZo8b5DscQsinVKLJ+GICa/qGF1+C/hy34f7Fk2kCHYspDxOfMreAoMI2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:44:55.968135Z"},"content_sha256":"60020077f2e63bfda1ffd068573d7d4efba7ed120113d5bd0374225561652263","schema_version":"1.0","event_id":"sha256:60020077f2e63bfda1ffd068573d7d4efba7ed120113d5bd0374225561652263"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:2JXUKCJTAASZQTJAFMI2PP24QZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hans-Goerg Roos, Yanjie Mei, Yao Cheng","submitted_at":"2020-12-07T10:00:40Z","abstract_excerpt":"In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a class of layer-adapted meshes including Shishkin-type and Bakhvalov-type meshes and the implicit $\\theta$-scheme in time. For piecewise tensor-product polynomials of degree $k$ we obtain uniform or almost uniform error estimates with respect to space of order $k+1/2$ in some energy norm and optimal error estimates with respect to time. Our analysis is based on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03560","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/2012.03560/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Wp2qwdgx28UiZuMRbyThpoR5DUD6Ie7iH3Utbkq0QD/12zN6+WXCiiY2H4ThqaQRAs/XwjI231/njlxp2NgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:44:55.968532Z"},"content_sha256":"6ef073a2d66303e38f1643ba17f992b7da5afe42a6d1bbbf363b571d49f94b3b","schema_version":"1.0","event_id":"sha256:6ef073a2d66303e38f1643ba17f992b7da5afe42a6d1bbbf363b571d49f94b3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JXUKCJTAASZQTJAFMI2PP24QZ/bundle.json","state_url":"https://pith.science/pith/2JXUKCJTAASZQTJAFMI2PP24QZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JXUKCJTAASZQTJAFMI2PP24QZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T08:44:55Z","links":{"resolver":"https://pith.science/pith/2JXUKCJTAASZQTJAFMI2PP24QZ","bundle":"https://pith.science/pith/2JXUKCJTAASZQTJAFMI2PP24QZ/bundle.json","state":"https://pith.science/pith/2JXUKCJTAASZQTJAFMI2PP24QZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JXUKCJTAASZQTJAFMI2PP24QZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:2JXUKCJTAASZQTJAFMI2PP24QZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0d851b989260069faa1880e38290c56f000cfcb855fc859a3d99bcb1fed8f58f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-12-07T10:00:40Z","title_canon_sha256":"57c382afe59e89ab271511c3aaf82e74efe8d3db38413b74075fe94de90e8ec0"},"schema_version":"1.0","source":{"id":"2012.03560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03560","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03560v1","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03560","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"2JXUKCJTAASZ","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"pith_short_16","alias_value":"2JXUKCJTAASZQTJA","created_at":"2026-07-05T01:57:31Z"},{"alias_kind":"pith_short_8","alias_value":"2JXUKCJT","created_at":"2026-07-05T01:57:31Z"}],"graph_snapshots":[{"event_id":"sha256:6ef073a2d66303e38f1643ba17f992b7da5afe42a6d1bbbf363b571d49f94b3b","target":"graph","created_at":"2026-07-05T01:57:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.03560/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a class of layer-adapted meshes including Shishkin-type and Bakhvalov-type meshes and the implicit $\\theta$-scheme in time. For piecewise tensor-product polynomials of degree $k$ we obtain uniform or almost uniform error estimates with respect to space of order $k+1/2$ in some energy norm and optimal error estimates with respect to time. Our analysis is based on","authors_text":"Hans-Goerg Roos, Yanjie Mei, Yao Cheng","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-12-07T10:00:40Z","title":"The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03560","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:60020077f2e63bfda1ffd068573d7d4efba7ed120113d5bd0374225561652263","target":"record","created_at":"2026-07-05T01:57:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0d851b989260069faa1880e38290c56f000cfcb855fc859a3d99bcb1fed8f58f","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-12-07T10:00:40Z","title_canon_sha256":"57c382afe59e89ab271511c3aaf82e74efe8d3db38413b74075fe94de90e8ec0"},"schema_version":"1.0","source":{"id":"2012.03560","kind":"arxiv","version":1}},"canonical_sha256":"d26f4509330025984d202b11a7bf5c8655e5c22ddd5fd30d626c26695fde3a9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d26f4509330025984d202b11a7bf5c8655e5c22ddd5fd30d626c26695fde3a9e","first_computed_at":"2026-07-05T01:57:31.113408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:57:31.113408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mzHe5akgUINLzD3BuNdxM7ObwfgwMKU2YSOup3h52OU9WI6lvdyf+XJt1euDzI/KRKNECg084/MUqsEziKpXBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:57:31.113801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.03560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60020077f2e63bfda1ffd068573d7d4efba7ed120113d5bd0374225561652263","sha256:6ef073a2d66303e38f1643ba17f992b7da5afe42a6d1bbbf363b571d49f94b3b"],"state_sha256":"ee791564f002a105ae6238816814293082048f872b9c3c52e8f9798750e82e9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qrKo9E/5quAI4APCiXvN+G7NwMqpYdyAfJnWAyj4Lbi3rjQAvXafUvfA7QXsuJwHy4b/Fpo/dogeihqk1YwYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:44:55.970516Z","bundle_sha256":"524dce068ba173e09b925b64b0466aea749f6ca3d36088fda059ddb1ad067244"}}