A lifted local Galerkin method for solving the reaction-diffusion equations on implicit surfaces

The reaction-diffusion equations models on surfaces have received growing interest and have been applied to simulate the physical processes and chemical reactions on ultra-thin materials, solid surfaces and biological films. In this article, we present a lifted local Galerkin method for solving the reaction-diffusion equations on implicit surfaces. The basic idea of proposed method is to discretize the equations on tangent plane of each surface node. Based on this idea, for each surface node, we first construct the local triangulation mesh via using this node and lifted points of its neighborhood on the tangent plane for this node. After setting a constant extension of surface data between each neighborhood and lifted point, we construct the discrete scheme by a local Galerkin method. Finally, the convergence tests and some applications in engineering science of the proposed method are shown to verify the feasibility and correction.