{"paper":{"title":"The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ignacio Muga, Kristoffer G. van der Zee, Matthew J. W. Tyler","submitted_at":"2018-08-14T05:57:42Z","abstract_excerpt":"We propose and analyse a minimal-residual method in discrete dual norms for approximating the solution of the advection-reaction equation in a weak Banach-space setting. The weak formulation allows for the direct approximation of solutions in the Lebesgue $L^p$-space, $1<p<\\infty$. The greater generality of this weak setting is natural when dealing with rough data and highly irregular solutions, and when enhanced qualitative features of the approximations are needed.\n  We first present a rigorous analysis of the well-posedness of the underlying continuous weak formulation, under natural assump"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04542","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"}