Stability of spatial interpolation functions in finite element one‐dimensional kinematic wave rainfall‐runoff models

Abstract

This paper analyzes the stability of linear, lumped, quadratic, and cubic spatial interpolation functions in finite element one‐dimensional kinematic wave schemes for simulation of rainfall‐runoff processes. Galerkin’s residual method transforms the kinematic wave partial differential equations into a system of ordinary differential equations. The stability of this system is analyzed using the definition of the norm of vectors and matrices. The stability index, or singularity of the system, is computed by the Singular Value Decomposition algorithm. The oscillation of the solution of the finite element one‐dimensional kinematic wave schemes results both from the sources, and from the multiplication operator of oscillation. The results of computation experiment and analysis show the advantage and disadvantage of different types of spatial interpolation functions when FEM is applied for rainfall‐ runoff modeling by kinematic wave equations.