{"product_id":"a-comparison-of-hp-adaptive-strategies-for-elliptic-partial-differential-equations-long-version-9781493745166","title":"A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version)","description":"\u003cp\u003e • Author(s): Nist\u003cbr\u003e • Publisher: Createspace Independent Publishing Platform\u003cbr\u003e • Publisher Imprint: Createspace Independent Publishing Platform\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations because it can achieve a convergence rate that is exponential in the number of degrees of freedom. hp-FEM allows for refinement in both the element size, h, and the polynomial degree, p. Like adaptive refinement for the h 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 can not simultaneously determine whether it is better to do the refinement by h or by p. Several strategies for making this determination have been proposed over the years. In this paper we summarize these strategies and present the results of a numerical experiment to study the convergence properties of these strategies.\u003c\/p\u003e","brand":"Createspace Independent Publishing Platform","offers":[{"title":"Paperback","offer_id":45498667335831,"sku":"9781493745166","price":1425.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781493745166.webp?v=1767449313","url":"https:\/\/atlanticbooks.com\/products\/a-comparison-of-hp-adaptive-strategies-for-elliptic-partial-differential-equations-long-version-9781493745166","provider":"Atlantic Books","version":"1.0","type":"link"}