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An arbitrary order Reconstructed Discontinuous Approximation to Fourth-order Curl Problem (2406.05624v1)
Published 9 Jun 2024 in math.NA and cs.NA
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 L2 norm and show numerical results to verify the theoretical analysis.