An arbitrary order Reconstructed Discontinuous Approximation to Fourth-order Curl Problem

Ruo Li; Qicheng Liu; Shuhai Zhao

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arXiv · 2406.05624

An arbitrary order Reconstructed Discontinuous Approximation to Fourth-order Curl Problem

Ruo Li·Qicheng Liu·Shuhai Zhao

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Abstract

We present an arbitrary order discontinuous Galerkin finite element method for solving the fourth-order curl problem using a reconstructed discontinuous approximation method. It is based on an arbitrarily high-order approximation space with one unknown per element in each dimension. The discrete problem is based on the symmetric IPDG method. We prove a priori error estimates under the energy norm and the L^2 norm and show numerical results to verify the theoretical analysis.

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Ruo Li, Qicheng Liu, Shuhai Zhao. 2024-06-09. An arbitrary order Reconstructed Discontinuous Approximation to Fourth-order Curl Problem. https://arxiv.org/abs/2406.05624

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