{"paper":{"title":"On the exponent of exponential convergence of the $p$-version FEM spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Zhaonan Dong","submitted_at":"2017-04-26T10:26:23Z","abstract_excerpt":"We study the exponent of the exponential rate of convergence in terms of the number of degrees of freedom for various non-standard {$p$-version} finite element spaces employing reduced cardinality basis. More specifically, we show that serendipity finite element methods and discontinuous Galerkin finite element methods with total degree $\\mathcal{P}_p$ basis have a faster exponential convergence with respect to the number of degrees of freedom than their counterparts employing the tensor product $\\mathcal{Q}_p$ basis for quadrilateral/hexahedral elements, for piecewise analytic problems under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08046","kind":"arxiv","version":3},"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"}