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Computational Mathematics

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Computational Mathematics

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Research Frontiers in Discontinuous Galerkin Methods for Hyperbolic Conservation Laws

High-order discretization schemes for capturing shock discontinuities and preserving physical constraints in nonlinear hyperbolic equations.

Adaptive Mesh Refinement in Shock-Capturing DG Schemes
Entropy Stability and Positivity Preservation in High-Order DG
Implicit Time Integration for Stiff Hyperbolic Systems
Subcell Limiting Strategies for Multi-Dimensional Conservation Laws
DG Methods on Unstructured and Hybrid Mesh Topologies
Sparse Grid Collocation for Uncertain Hyperbolic PDEs
Superconvergence Phenomena in Discontinuous Galerkin Approximations
Machine Learning-Accelerated Flux Reconstruction in DG
Well-Balanced Schemes for Hyperbolic Systems with Source Terms
Local Discontinuous Galerkin Methods for Nonlinear Wave Phenomena

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