{"paper":{"title":"Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Espen R. Jakobsen, F\\'elix del Teso, J{\\o}rgen Endal","submitted_at":"2018-01-22T15:45:19Z","abstract_excerpt":"We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \\partial_t u-\\mathfrak{L}^{\\sigma,\\mu}[\\varphi(u)]=f \\quad\\quad\\text{in}\\quad\\quad \\mathbb{R}^N\\times(0,T), $$ where $\\mathfrak{L}^{\\sigma,\\mu}$ is a general symmetric diffusion operator of L\\'evy type and $\\varphi$ is merely continuous and non-decreasing. We then use this theory to prove convergence for many different numerical schemes. In the nonlocal case most of the results are completely new. Our theory covers strongly degenerate Stefan problems, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07148","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"}