非线性对流扩散方程的三层隐-显hp-局部间断Galerkin有限元方法

The three-step implicit-explicit hp-local discontinuous Galerkin finite element method for nonlinear convection diffusion problems

使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的三层隐-显hp-LDG方法的误差估计.对Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果.

By using the general framework introduced in Arnod et al. and the new method dealting with the nonlinear convection term, the error estimates of three-step implicit-explicit hp-LDG method for nonlinear convection diffusion problems are obtained. The numerical example for the nonlinear Burgers equation is presented in the paper. The numerical results verify the theoretical results obtained in this paper.