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

TL;DR

This paper introduces a high-order discontinuous Galerkin finite element method for solving the complex fourth-order curl problem, providing theoretical error estimates and numerical validation.

Contribution

It develops an arbitrary order reconstructed discontinuous approximation method based on symmetric IPDG for the fourth-order curl problem, with proven error bounds.

Findings

The method achieves optimal error estimates in energy and L^2 norms.

Numerical results confirm the theoretical error bounds.

The approach is flexible for high-order approximations.

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.