{"paper":{"title":"A space-time finite element method for fractional wave problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Binjie Li, Hao Luo, Xiaoping Xie","submitted_at":"2018-03-09T09:44:30Z","abstract_excerpt":"This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \\gamma $ ($1<\\gamma<2$). We establish the stability of this method, and derive the optimal convergence in the $ H^1(0,T;L^2(\\Omega)) $-norm and suboptimal convergence in the discrete $ L^\\infty(0,T;H_0^1(\\Omega)) $-norm. Furthermore, we discuss the performance of this method in the case that the solution has singularity at $ t= 0 $, and show that optimal convergence rate with respect to the $ H^1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03437","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"}