Mitchell, W.
(2015),
How High a Degree is High Enough for High Order Finite Elements?, International Conference on Computational Science, Reykjavík, -1, [online], https://doi.org/10.1016/j.procs.2015.05.235
(Accessed December 9, 2024)
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How High a Degree is High Enough for High Order Finite Elements?
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Abstract
High order finite element methods can solve partial differential equations more efficiently than low order methods. But how large of a polynomial degree is beneficial? This paper addresses that question through a case study of three problems representing problems with smooth solutions, problems with steep gradients, and problems with singularities. It also contrasts h-adaptive, p-adaptive, and hp-adaptive refinement. The results indicate that for low accuracy requirements, like 1% relative error, h-adaptive refinement with relatively low order elements is sufficient, and for high accuracy requirements, p-adaptive refinement is best for smooth problems and hp-adaptive refinement with elements up to about 10th degree is best for other problems.Proceedings Title
International Conference on Computational Science
Volume
51
Conference Dates
June 1-3, 2015
Conference Location
Reykjavík
Pub Type
Conferences
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Keywords
finite elements, high order methods, hp-FEM
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Created December 31, 2014, Updated October 14, 2020