Published In
Results in Applied Mathematics
Document Type
Article
Publication Date
11-4-2024
Subjects
Differential geometry -- Regge metrics
Abstract
Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to studying the convergence of the finite element lifting of a generalized (distributional) Gauss curvature defined using a metric tensor approximation in the Regge finite element space. Specifically, we investigate the interplay between the polynomial degree of the curvature lifting by Lagrange elements and the degree of the metric tensor in the Regge finite element space. Previously, a superconvergence result, where convergence rate of one order higher than expected, was obtained when the approximate metric is the canonical Regge interpolant of the exact metric. In this work, we show that an even higher order can be obtained if the degree of the curvature lifting is reduced by one polynomial degree and if at least linear Regge elements are used. These improved convergence rates are confirmed by numerical examples.
Rights
Copyright (c) 2024 The Authors Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 International License.
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DOI
10.1016/j.rinam.2024.100511
Persistent Identifier
https://archives.pdx.edu/ds/psu/42706
Citation Details
Gopalakrishnan, J., Neunteufel, M., Schöberl, J., & Wardetzky, M. (2024). On the improved convergence of lifted distributional Gauss curvature from Regge elements. Results in Applied Mathematics, 24, 100511.