# ME 697F - Galerkin Methods for Fluid Dynamics - Spring 2010

## Class News

Here I will try and post class related, dated messages and/or clarifications for your information. I suggest you check it periodically (weekly or more) just in case.
1. 01/20/10: Hi Guys! Well we made it throught he FEM Primer notes more or less. I realize I did not go over every single topic/example in those notes nor did I explain what I did go over totally clearly. But I think if you read those notes carefully (more than once for sure) and paid attention in class you should have some feel for the following important FEM related topics: (a) vector (function) spaces, (b) variational (weak) form of BVP, (c) Galerkin method, and (d) piecewise polynomial approximation. For second-order BVP's, such as Poisson equation, we will require solutions to be members of the H^1 function space admitting functions that together with their first derivatives are square integrable. For load function spaces we require L^2 (just the function is square integrable). The variational form of BVP is obtained by multiplying the BVP by a test function in H^1, integrating the PDE over the domain, and applying integration by parts, which takes one derivative off of the dependent variable and puts it on the smooth test function. By choosing the test function to be equivalent to the presumed solution function (basis) we have the Galerkin method. A piecewise polynomial approximation applied to this results in a linear system of equations. We are now in the middle of the details of this process and you should be reading Chapter 5 of Schafer. Also please study details of the myfem1d.f90 code and note it currently using gnuplot for postprocessing (see Jeff for details on how to compile this program).
2. 02/3/10: Hi. I hope to have HW1 graded and returned to you by the time your next HW is due. It is not that they are taking me long to grade, it is just lecture preparation is consumingn all my time even thought it may not show. On HW2 please do a nice job with the write-up (type-up) as I hope to use the best of your work as solutions for future offerings. Also, please feel free to make improvements in the Fortran (2D) code e.g. pre- and post-processing, inputs, outputs, etc. as I plan to re-use the most improved (cleanest) version for future offerings. Don't forget to download the notes for this week from the website.