{"paper":{"title":"A Priori $hp$-estimates for Discontinuous Galerkin Approximations to Linear Hyperbolic Integro-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amiya K. Pani, Samir Karaa, Sangita Yadav","submitted_at":"2014-01-22T02:04:39Z","abstract_excerpt":"An $hp$-discontinuous Galerkin (DG) method is applied to a class of second order linear hyperbolic integro-differential equations. Based on the analysis of an expanded mixed type Ritz-Volterra projection, {\\it a priori} $hp$-error estimates in $L^{\\infty}(L^2)$-norm of the velocity as well as of the displacement, which are optimal in the discretizing parameter $h$ and suboptimal in the degree of polynomial $p$ are derived. For optimal estimates of the displacement in $L^{\\infty}(L^2)$-norm with reduced regularity on the exact solution, a variant of Baker's nonstandard energy formulation is dev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5539","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"}