Document Type

Article

Publication Date

10-14-2020

Abstract

We study the finite element approximation of the Kirchhoff plate equation on domains with curved boundaries using the Hellan-Herrmann-Johnson (HHJ) method. We prove optimal convergence on domains with piecewise Ck+1 boundary for k ≥ 1 when using a parametric (curved) HHJ space. Computational results are given that demonstrate optimal convergence and how convergence degrades when curved triangles of insufficient polynomial degree are used. Moreover, we show that the lowest order HHJ method on a polygonal approximation of the disk does not succumb to the classic Babuška paradox, highlighting the geometrically nonconforming aspect of the HHJ method.

Publication Source (Journal or Book title)

SIAM Journal on Numerical Analysis

First Page

2829

Last Page

2855

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