中文摘要：

对于非结构三角形网格上Hamilton—Jacobi（H—J）方程的数值方法的构造，主要困难在于数值通量的选择和高精度插值多项式的构造．利用Abgrall提出的数值通量，在每个三角形单元上构造高阶插值多项式，得到了一个求解H—J方程的高阶精度格式．数值实验结果表明，该格式具有较高的精度和较好的分辨率．

英文摘要：

About the construction of numerical methods in solving H-J equations on unstructured triangular meshes, the difficulty is mainly the choice of numerical flux and the construction of the high-order interpolation polynomials. By using the munerical flux of H-J equations which Abgrall proposed, a high-order scheme for H-J equations is obtained by constructing the high-order interpolation polynomials on every triangular mesh. The numerical experiment resuhs show that the constructed schemes are of high-order accuracy in smooth regions and good resolution.