Comparison analysis between meshless radial basis function collocation method and finite element method

Comparison analysis between meshless Radial Basis Function Collocation Method and Finite Element Method is conducted in this work. Models for both steady and unsteady versions of Poisson and Stokes equation with various types of boundary conditions are built. The domains studied are square and L-shaped. The mesh, or the number of nodes inside these domains is gradually increased to observe the convergence properties of the methods. For the meshless method, a novel least square error calculation technique is presented to make the error comparison against Finite Element Method fair. Additionally, the shape factor optimization algorithm which minimizes the root mean square error is implemented for the meshless model to yield the most accurate results available. Then, the performances of both methods are compared considering several parameters. These parameters are chosen to be: accuracy by comparing least square error, root mean square error and maximum relative error; stability by comparing condition numbers; robustness by comparing convergence rates; computational cost by comparing runtimes; and ease of implementation.