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Author

Meng-Ping Zhang

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Preprint Oct 2026

Energy Stability and Error Estimates for a Globally Divergence-Free DG Method of Arbitrary Order

We propose and analyze an arbitrary-order globally divergence-free (GDF) discontinuous Galerkin (DG) method for the two-dimensional linear magnetic induction equation on unstructured triangular meshes. To the best of our knowledge, this is the first work to provide a rigorous energy-based analysis of high-order GDF-DG...

Yu-Chang Liu, Yan Jiang, Meng-Ping Zhang · 0 citations
Preprint Oct 2026

High-Order Fully Discrete Entropy-Stable DG Methods with Compact Explicit Single-Step Time Discretizations

We develop a unified framework for high-order, fully discrete entropy-stable discontinuous Galerkin (DG) methods with compact explicit single-step time discretizations. At the end of each time step, the preliminary DG polynomial is scaled toward its cell average to enforce a strong cell entropy inequality while preserv...

Yu-Chang Liu, Yan Jiang, Meng-Ping Zhang · 0 citations

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