With the advance of computers, the numerical solution of partial differential equations plays an increasingly important role in engineering design and scientific research. However, for three decades people have been doing something wrong in Computational Fluid Dynamics and Computational Electromagnetics. This talk will reveal that many difficulties in CFD and CEM, such as oscillations, instabilities and spurious solutions, are really caused by wrong formulations. That is, finite element analyses in fluid dynamics (in general, for non self-adjoint PDEs) are mistakenly based on the Galerkin method; almost all numerical methods in electromagnetics mistakenly ignore the divergence equations. In this talk it will be shown that the least squares finite element method (LSFEM) is a correct direction to go.