A High-Order Runge-Kutta Discontinuous Galerkin Method for The Two-Dimensional Wave Equation

• Main Authors: Meng-HanLi, 李孟翰
• Other Authors: Min-Hung Chen
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/60562488311569777411

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 98 === In this work, we develop a high-order Runge-Kutta Discontinuous Galerkin (RKDG) method to solve the two-dimensional wave equations. We use DG methods to discretize the equations with high order elements in space, and then we use the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme to solve the resulting semi-discrete equations. To discretize the equaiotns in spaces, we use the quadrilateral elements and the Q^k-polynomials as basis functions. The scheme achieves full high-order convergence in time and space while keeping the time-step proportional to the spatial mesh-size. Numerical results are presented that confirm the expected convergence properties. When all the local spaces contain the polynomials of degree p,the numerical experiments show that the numerical solution converges with order p+1.