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How High a Degree is High Enough for High Order Finite Elements?



William F. Mitchell


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
Conference Dates
June 1-3, 2015
Conference Location


finite elements, high order methods, hp-FEM


Mitchell, W. (2015), How High a Degree is High Enough for High Order Finite Elements?, International Conference on Computational Science, Reykjavík, -1, [online], (Accessed April 21, 2024)
Created December 31, 2014, Updated October 14, 2020