Abstract
In order to solve 3D convection-diffusion-reaction problems accurately and efficiently, we study the dimension coupling method (DCM) by combining the finite element method (FEM) with the improved element-free Galerkin (IEFG) method. The idea of the dimension splitting method is introduced into the governing equation of such problems, thus a series of 2D forms can be obtained by splitting the original 3D problem. The IEFG method is used to discretize these 2D problems, thus the discretized equations of 2D forms can be obtained by using the corresponding weak form. In the dimension splitting direction, the FEM is used to couple these discretized equations, thus final linear equations of original 3D problem can be obtained. The formula of the relative error is given, and the convergence of the DCM is proved numerically. The results of four numerical examples show that the advantage of the DCM is its highly computational efficiency.
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