A new method for some advection equations is derived and analyzed, where the finite element method is constructed by using spline. A proper spline subspace is discussed for satisfying boundary conditions. Meanwhile, in order to get more accuracy solutions, spline method is connected with finite element method. Furthermore, the stability and convergence are discussed rigorously. Two numerical experiments are also presented to verify the theoretical analysis.

中文翻译：

---

基于样条法的二维线性平流方程有限元法

推导并分析了一些对流方程的新方法，其中有限元方法是利用样条构造的。讨论了满足边界条件的适当样条子空间。同时，为了得到更精确的解，样条法与有限元法相结合。此外，对稳定性和收敛性进行了严格的讨论。还提出了两个数值实验来验证理论分析。