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CB-pMOR is designed to deal with large-scale problems for which full-order solves are not affordable in a reasonable time frame or parameters\u2019 variations induce topology changes that prevent the application of monolithic pMOR techniques. We rely on the partition-of-unity method to devise global approximation spaces from local reduced spaces, and on Galerkin projection to compute the global state estimate. We propose a randomized data compression algorithm based on oversampling for the construction of the components\u2019 reduced spaces: the approach exploits random boundary conditions of controlled smoothness on the oversampling boundary. We further propose an adaptive residual-based enrichment algorithm that exploits global reduced-order solves on representative systems to update the local reduced spaces. We prove exponential convergence of the enrichment procedure for linear coercive problems; we further present numerical results for a two-dimensional nonlinear diffusion problem to illustrate the many features of our methodology and demonstrate its effectiveness.<\/jats:p>","DOI":"10.1137\/22m148402x","type":"journal-article","created":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T14:35:24Z","timestamp":1686839724000},"page":"A1300-A1331","source":"Crossref","is-referenced-by-count":21,"title":["Localized Model Reduction for Nonlinear Elliptic Partial Differential Equations: Localized Training, Partition of Unity, and Adaptive Enrichment"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4245-6586","authenticated-orcid":true,"given":"Kathrin","family":"Smetana","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3134-3730","authenticated-orcid":true,"given":"Tommaso","family":"Taddei","sequence":"additional","affiliation":[{"name":"IMB, UMR 5251, Univ Bordeaux, 33400 Talence, France INRIA Bordeaux Sud-Ouest, Team MEMPHIS, 33400 Talence, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,15]]},"reference":[{"key":"ref1","unstructured":"F. 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