Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by planar triangles and careful design of numerical fluxes. The schemes are proven to be energy stable. Various numerical experiments are provided to validate the new schemes.

翻译：本文发展了用于求解静态二维流形上二阶及四阶时变偏微分方程的局部间断伽辽金方法。通过平面三角形网格对曲面进行三角剖分，并精心设计数值通量，这些格式具有二阶精度。理论证明了该格式的能量稳定性，并通过多种数值实验验证了新格式的有效性。