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A semi-analytical method so-called the Scaled Boundary Finite-Element Method (SBFEM) is employed for solving two-dimensional steady-state reaction-diffusion equation with constant diffusion and decay coefficients which is widely used in contaminant transfer, chemical engineering and heat transfer problems. This method has been successfully applied to various problems of engineering such as elastodynamics, fracture mechanics and seepage. This method has advantages of both boundary element method and finite-element method. Only the boundary is discretized reducing the spatial dimension by one. Unlike the boundary element method no fundamental solution is required. Interpolation over the boundaries is approximated using shape functions same in the finite-element method. Singularities, anisotropic problems, non-homogeneities satisfying similarity and radiation condition at infinity used in modeling unbounded domains are simply modeled by this technique. In this study, after derivation of the scaled boundary finite-element formulations for reaction–diffusion equation, solution procedures based on dynamic-stiffness matrix are proposed. The accuracy and performance of the SBFEM is evaluated using numerical examples. There are a reasonable agreement between the results of the scaled boundary finite-element method, the analytical solutions and the popular numerical approaches.

Keywords: Scaled Boundary Finite-Element Method, Diffusion, reaction, Discretization

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