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math.NA2025
An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions
Yangxin Fu, Yan Jiang, Siyang Wang
We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach inte…
math.NA2024
Upwind summation-by-parts finite differences: error estimates and WENO methodology
Yan Jiang, Siyang Wang
High order upwind summation-by-parts finite difference operators have recently been developed. When combined with the simultaneous-approximation-term method to impose boundary cond…