TY - JOUR
T1 - A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws
AU - Yaguang Gu & Guanghui Hu
JO - Communications in Computational Physics
VL - 3
SP - 829
EP - 851
PY - 2017
DA - 2017/09
SN - 22
DO - http://doi.org/10.4208/cicp.OA-2016-0088
UR - https://global-sci.org/intro/article_detail/cicp/9983.html
KW - 
AB - <p style="text-align: justify;">We introduce a third order adaptive mesh method to arbitrary high order
Godunov approach. Our adaptive mesh method consists of two parts, i.e., mesh-redistribution
algorithm and solution algorithm. The mesh-redistribution algorithm is
derived based on variational approach, while a new solution algorithm is developed to
preserve high order numerical accuracy well. The feature of proposed Adaptive ADER
scheme 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 with
adaptive mesh method, and 3). high resolution and non-oscillatory numerical solutions
are obtained successfully when there are shocks in the solution. A variety of
numerical examples show the feature well.</p>