{"paper":{"title":"On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"G. S. Payette, J. N. Reddy, K. B. Nakshatrala","submitted_at":"2011-08-03T22:21:45Z","abstract_excerpt":"The main aim of this paper is to document the performance of $p$-refinement with respect to maximum principles and the non-negative constraint. The  model problem is (steady-state) anisotropic diffusion with decay (which  is a second-order elliptic partial differential equation). We considered  the standard single-field formulation (which is based on the Galerkin  formalism) and two least-squares-based mixed formulations. We have  employed non-uniform Lagrange polynomials for altering the polynomial order in each element, and we have used $p = 1, ..., 10$.\n  It will be shown that the violation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0952","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"}