finite element vs. finite difference
Sorry for the dummy question, but i am a beginner in CFD. Could anybody shortly explain the main differences between finite elemente and finit differencing methods, i mean advantages and drawbacks of them in CFD problem solutions?
Thank you in advance Zoltan Turzo Assistant Professor University of Miskolc 
Re: finite element vs. finite difference
(1). The finitedifference method uses Taylor's series expansion to approximate the derivatives terms in the governing equations. Results are then obtained by solving a set of resulting algebraic equations. (2). The finiteelement method assumes that the solution within an element of volume will take certain functional form in the first place. It then uses minimization processes, variational principles, weighted residual methods to obtain the solutions in the assumed functional form. (3). The finitedifference method is consistent with the original definition of derivatives, and is widely used in all fields of physics. (4). The finiteelement method has been very successful in the solid mechanics, structure analysis. The ability to handle complex structure and geometry is widely recognized. (5). The main difficulty with finiteelement method has been the lack of sound physical foundation. The memory requirement for solving large matrix equations was also very high. (6). The finitevolume method tries to solve the integral form of the governing equation over a small finite volume. Approximations are applied to the integration in order to derive the algebraic equations. These are solved in the way similar to the finitedifference method. Using this approach and unstructured mesh similar to the finiteelement method, problems with complex geometry can be handled easily. (7). Solutions to the highly nonlinear, coupled, partialdifferential equations are very hard to obtain. Therefore, any method is a good method, if good solution can be obtained. ( The war between the finitedifference and the finiteelement methods was long over in 70's ). You are free to invent new methods to solve CFD problems.

Re: finite element vs. finite difference
Thank you for your answer. It was very usefull for me.

All times are GMT 4. The time now is 03:36. 