无网格方法关于导数计算的程序验证

为了提高无网格方法对空间导数的数值计算能力，提出并论证了新的适用于直角坐标系、柱坐标系和球坐标系的空间导数无网格算法。基于数值解与理论解的对比分析，对数值误差和收敛性进行了后验评估。评估结果表明:该算法对函数和导数的估计均为2阶精度，支撑域尺度对数值误差的大小有一定影响，但不影响数值计算的精度等级。在离散尺度h为0.01的条件下，对所选函数及其导数的数值计算相对误差不大于0.65%。 

Code verification of mesh free method with computation of derivatives

In order to improve the approximation of spatial derivatives without meshes, a set of mesh free method for spatial derivatives was developed, which agreed well with the Cartesian, cylindrical and spherical coordinates. Based on the comparisons between numerical and theoretical solutions, the errors and convergences were assessed by a posteriori method, showing that the approximations for functions and derivatives were of the second order accurate, and the scale of the support domain had some influences on numerical errors but not on accuracy orders. With a discrete scale h being 0.01, the relative errors of the numerical simulation for the selected functions and their derivatives were within 0.65%.