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A new control volume finite element (CVFE) method is formulated from integral form of conservation laws, i.e. conservation of mass, for overland flows under kinematic wave assumption. With an approximation m v h = , the system becomes a nonlinear system with unknowns such as flow velocity and flow depth. The differential system of error equations is obtained by linearization of conservation laws in their discrete form for a control volume and an error analysis is obtained using Fourier or von Neumann method. Four nodal quadrilateral or bilinear rectangular shape functions are used to evaluate local and global matrices in the resulting control volume finite element (CVFE) formulation. The nodal amplification factors using coefficient method are compared with those obtained using exact method or eigen-value analysis. The nodal amplification factors show a straight line behavior for all of the wavenumbers for explicit, semi-implicit, and implicit control volume finite element schemes.