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Numerical Analysis

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Numerical Analysis

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Research Frontiers in Discontinuous Galerkin Methods

Investigation of discontinuous polynomial spaces for discretizing hyperbolic and mixed-type PDEs with superior stability properties.

High-Order Accuracy in Shock-Capturing Discontinuous Galerkin Schemes
Implicit Time Integration and Stability in DG Frameworks
Adaptive Mesh Refinement Strategies for Discontinuous Solutions
Superconvergence Phenomena in Discontinuous Galerkin Methods
Multiphase Flow Simulation via DG Formulations
Hybridized Discontinuous Galerkin Methods and Computational Efficiency
Entropy Stability and Well-Posedness in Nonlinear DG Schemes
Localized Basis Functions in High-Dimensional DG Approximations
Discontinuous Galerkin Methods for Hyperbolic Conservation Laws
Machine Learning Enhanced DG Error Estimation and Prediction

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