The HCVEFG method for 3D steady convection–diffusion–reaction problems

In this paper, a hybrid complex variable element-free Galerkin (HCVEFG) method is proposed for solving three-dimensional (3D) steady convection–diffusion–reaction equations. By introducing the dimension splitting method (DSM), a 3D convection–diffusion–reaction problem is changed into a series of two-dimensional (2D) ones. For each 2D form, the improved complex variable moving least-squares (ICVMLS) method is applied to obtain the required approximation shape functions, and the penalty method is used to apply the essential boundary conditions, thus we can obtain the 2D discretized equations by using the improved complex variable element-free Galerkin (ICVEFG) method. The finite difference method (FDM) is used in one-dimensional splitting direction. Thus, the final solution formula about the numerical solution for 3D convection–diffusion–reaction problem can be obtained. Three numerical examples show that the HCVEFG algorithm can cut down the CPU cost of the improved element-free Galerkin (IEFG) method greatly for solving 3D steady convection–diffusion–reaction problems.