{"paper":{"title":"A Positivity-Preserving Limiting Strategy for Locally-Implicit Lax-Wendroff Discontinuous Galerkin Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Caleb Logemann, Camille Felton, Ian Pelakh, James A. Rossmanith, Mariana Harris, Stefan Nelson","submitted_at":"2018-06-18T15:12:03Z","abstract_excerpt":"Nonlinear hyperbolic conservation laws admit singular solutions such as shockwaves (discontinuities in conserved variables), rarefaction waves (discontinuities in derivatives), and vacuum states (loss of strong hyperbolicity). When ostensibly high-order numerical methods are applied in such solution regimes, unphysical oscillations present themselves that can lead to large errors and a breakdown of the numerical simulation. In this work we develop a new Lax-Wendroff discontinuous Galerkin (LxW-DG) method with a limiting strategy that keeps the solution non-oscillatory and positivity-preserving"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06756","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"}