  Steady and unsteady Poisson and Stokes equations are solved using mesh
dependent Finite Element Method and meshless Radial Basis Function Collocation
Method to compare the performances of these two numerical techniques across
several criteria. The accuracy of Radial Basis Function Collocation Method with
multiquadrics is enhanced by implementing a shape parameter optimization
algorithm. For the time-dependent problems, time discretization is conducted
using Backward Euler Method. The performances are assessed over the accuracy,
runtime, condition number, and ease of implementation criteria. Three kinds of
errors were calculated; least square error, root mean square error and maximum
relative error. To calculate the least square error while using meshless Radial
Basis Function Collocation Method, a novel technique is implemented. Imaginary
numerical solution surfaces are created and then the volume between those
imaginary surfaces and the analytic solution surfaces is calculated, enabling a
fair error calculation. Lastly, all solutions are put together and solution
trends are observed over the number of solution nodes vs. runtime, accuracy vs.
runtime, and accuracy vs. the number of nodes. The assessment indicates the
criteria under which Finite Element Method perform better and those when Radial
Basis Function Collocation Method outperforms its mesh dependent counterpart.
