The finite element methods for two and three-dimensional, steady-state inviscid and viscous flows are presented. For the inviscid flow, the finite element equations were derived from the conservation of mass. For the viscous flow, finite element equations were derived from the set of partial differential equations that satisfy the law of conservation of mass and momentums. The corresponding finite element computer programs were developed and verified by several examples that have exact solutions. In addition, the adaptive meshing technique is applied to increase the solution accuracy. The technique places small elements in the region of high velocity gradients, and at the same time, places larger elements in the other regions. The finite element computer programs were then used to predict detailed flow behaviors past ship hull including the pressure signature at different depth levels. Pressure signature solutions obtained both the inviscid and viscous flow analyses are in good agreement.
