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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 4
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Articles

Conforming and nonconforming harmonic finite elements

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Pages 569-584 | Received 11 May 2018, Accepted 20 Jul 2018, Published online: 01 Aug 2018
 

ABSTRACT

Instead of using the full polynomial space, a conforming and a nonconforming finite element methods are designed where only harmonic polynomials (a much smaller space) are employed in the computation. The conforming quadratic harmonic polynomial finite element is defined only on a special triangular grid. The nonconforming quadratic harmonic finite element is defined on general triangular grids. The optimal order of convergence is proved for both finite element methods, and confirmed by numerical computations. In addition, numerical comparisons with the standard conforming and nonconforming finite elements are presented.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Tatyana Sorokina is partially supported by the grant from the Simons Foundation [grant no 235411]. Shangyou Zhang is partially supported by The National Natural Science Foundation of China (NSFC) [grant no 11571023].

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