中文摘要：

针对双曲型守恒律方程问题，发展一种有效的自适应多分辨分析方法．通过对嵌套网格上的数值解构造离散多分辨分析，建立小波系数与多层嵌套网格点之间的对应关系．对于小波系数较大的网格点采用高精度WENO格式计算，其余区域则直接采用多项式插值．数值试验表明，该方法在保持原规则网格方法的精度和分辨率的同时，显著地减少计算的CPU时间．

英文摘要：

An efficient adaptive muhiresolution finite difference scheme is developed for hyperbolic conservation laws. Based on discrete multiresolution analysis of numerical solution on a nested grid structure, the scheme builds up an one-to-one relationship between wavelet coefficients with multiple nested grid point. At grid points where magnitude of wavelet coefficients are great, high-order WENO scheme is used for time evolution. While in the rest computational region, we use polynomial interpolation directly. Numerical experiments show that the method can reduce CPU time significantly, while maintaining accuracy and resolution of original regular grid method.