Abstract
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.
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