A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws (Communications in Computational Physics, 2017)
We introduce a third order adaptive mesh method to arbitrary high orderGodunov approach. Our adaptive mesh method consists of two parts, i.e., mesh-redistributionalgorithm and solution algorithm. The mesh-redistribution algorithm isderived based on variational approach, while a new solution algorithm is developed topreserve high order numerical accuracy well. The feature of proposed Adaptive ADERscheme includes that 1). all simulations in this paper are stable for large CFL number,2). third order convergence of the numerical solutions is successfully observed withadaptive mesh method, and 3). high resolution and non-oscillatory numerical solutionsare obtained successfully when there are shocks in the solution. A variety ofnumerical examples show the feature well.