{"paper":{"title":"Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NA","authors_text":"A. J. Roberts, G. A. Jarrad","submitted_at":"2016-02-03T04:06:43Z","abstract_excerpt":"Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed herein constructs a natural subgrid scale field adapted to the whole system out-of-equilibrium dynamics. Consequently, the macroscale discretisation is fully informed by the underlying microscale dynamics. We establish a new proof that in principle there exists an exact closure of the dynamics of a general class of reaction-advection-diffusion PDEs, and show how our approach constructs new systematic approximations to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01184","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"}