{"paper":{"title":"Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Espen R. Jakobsen, F\\'elix del Teso, J{\\o}rgen Endal","submitted_at":"2018-04-13T15:12:40Z","abstract_excerpt":"We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \\partial_t u-\\mathfrak{L}[\\varphi(u)]=f(x,t) \\qquad\\text{in}\\qquad \\mathbb{R}^N\\times(0,T), $$ where $\\mathfrak{L}$ is a general symmetric L\\'evy type diffusion operator. Included are both local and nonlocal problems with e.g. $\\mathfrak{L}=\\Delta$ or $\\mathfrak{L}=-(-\\Delta)^{\\frac\\alpha2}$, $\\alpha\\in(0,2)$, and porous medium, fast diffusion, and Stefan type nonlinearities $\\varphi$. By robust methods we mean that they converge even for nonsmooth solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04985","kind":"arxiv","version":2},"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"}