{"paper":{"title":"Crank-Nicolson Finite Element Discretizations for a 2D Linear Schr\\\"odinger-Type Equation Posed in a Noncylindrical Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"D. C. Antonopoulou, G. D. Karali, G. E. Zouraris, M. Plexousakis","submitted_at":"2011-10-18T16:30:43Z","abstract_excerpt":"Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\\\"odinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initial- and boundary-value problem is transformed into an equivalent one posed on a rectangular domain and is approximated by fully discrete, $L^2$-stable, finite element, Crank--Nicolson type schemes. We prove a global elliptic regularity theorem for complex elliptic boundary value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4046","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"}