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Softw."],"published-print":{"date-parts":[[2014,10,27]]},"abstract":"<jats:p>\n            The\n            <jats:italic>hp<\/jats:italic>\n            version of the finite element method (\n            <jats:italic>hp<\/jats:italic>\n            -FEM) combined with adaptive mesh refinement is a particularly efficient method for solving PDEs because it can achieve an exponential convergence rate in the number of degrees of freedom.\n            <jats:italic>hp<\/jats:italic>\n            -FEM allows for refinement in both the element size,\n            <jats:italic>h<\/jats:italic>\n            , and the polynomial degree,\n            <jats:italic>p<\/jats:italic>\n            . Like adaptive refinement for the\n            <jats:italic>h<\/jats:italic>\n            version of the finite element method, a posteriori error estimates can be used to determine where the mesh needs to be refined, but a single error estimate cannot simultaneously determine whether it is better to do the refinement by\n            <jats:italic>h<\/jats:italic>\n            or\n            <jats:italic>p<\/jats:italic>\n            . Several strategies for making this determination have been proposed over the years. These strategies are summarized, and the results of a numerical experiment to study the performance of these strategies is presented. It was found that the reference-solution-based methods are very effective, but also considerably more expensive, in terms of computation time, than other approaches. The method based on a priori knowledge is very effective when there are known point singularities. The method based on the decay rate of the expansion coefficients appears to be the best choice as a general strategy across all categories of problems, whereas many of the other strategies perform well in particular situations and are reasonable in general.\n          <\/jats:p>","DOI":"10.1145\/2629459","type":"journal-article","created":{"date-parts":[[2014,10,28]],"date-time":"2014-10-28T12:40:29Z","timestamp":1414500029000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":51,"title":["A Comparison of\n            <i>hp<\/i>\n            -Adaptive Strategies for Elliptic Partial Differential Equations"],"prefix":"10.1145","volume":"41","author":[{"given":"William F.","family":"Mitchell","sequence":"first","affiliation":[{"name":"National Institute of Standards and Technology"}]},{"given":"Marjorie A.","family":"McClain","sequence":"additional","affiliation":[{"name":"National Institute of Standards and Technology"}]}],"member":"320","published-online":{"date-parts":[[2014,10,27]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Adjerid S. 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