Bivariate Spline Finite Element Solver for Linear Hyperbolic Equations in Two-Dimensional Spaces

In this paper, a finite element method using bivariate spline on domains is proposed for solving linear hyperbolic equations in two-dimensional spaces. Bivariate spline space S_4^2,3 (Δ_mn^(2) ) is constructed. It not only satisfies homogeneous boundary constraints but also satisfies interpolating boundary conditions on type-2 triangulations. Two examples are shown to confirm the correctness of theoretical conclusions. This means that spline method is efficient and feasible to solve 2D linear hyperbolic equations.