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These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.<\/p>","DOI":"10.1090\/s0025-5718-99-01149-7","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"881-909","source":"Crossref","is-referenced-by-count":195,"title":["Local and parallel finite element algorithms based on two-grid discretizations"],"prefix":"10.1090","volume":"69","author":[{"given":"Jinchao","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aihui","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[1999,5,19]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics, Vol. 65","volume-title":"Sobolev spaces","author":"Adams, Robert A.","year":"1975"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF01385738","article-title":"A unified approach to a posteriori error estimation using element residual methods","volume":"65","author":"Ainsworth, Mark","year":"1993","journal-title":"Numer. 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