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An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. The numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.<\/jats:p>","DOI":"10.1137\/16m1083244","type":"journal-article","created":{"date-parts":[[2017,8,17]],"date-time":"2017-08-17T15:26:15Z","timestamp":1502983575000},"page":"A1531-A1557","source":"Crossref","is-referenced-by-count":23,"title":["A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations"],"prefix":"10.1137","volume":"39","author":[{"given":"Lin","family":"Mu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junping","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiu","family":"Ye","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0234-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(93)90025-5"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1994-1257573-4"},{"key":"atypb5","volume-title":"Least-Squares Finite Element Methods","author":"Bochev P.","year":"2009"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2536"},{"key":"atypb7","first-page":"1","volume":"00","author":"Bochev P.","year":"2011","journal-title":"Internat. 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