中文摘要：

针对勒让德谱元方法，构造了一类混合局部基函数，并证明了其线性无关特点。在此基础上，给出了一种勒让德谱元计算格式：在元素端点采用局部拉格朗日基函数，在元素内部采用调整后的局部勒让德多项式。进行了正确性和精度测试，数值实验结果表明该方法能够有效地实现高计算精度，且其计算矩阵比经典谱元方法更为简单，并具有良好的数据重用性和稀疏特点。

英文摘要：

A class of hybrid basis are designed for Legengre spectral element method and it＇s linear independence is proved. As a result, a new Legendre spectral element scheme is developed. The local lagrangian basis are used at the boundaries of the element, and the modified Legendre polynomials are adopted interiorly. Numerical tests show that high accuracy can be obtained with the hybrid local basis like the traditional spectral element method. What＇s more, the element matrices have sparsity characteristic and can be reused when the expansion order are different.