## Problem 22.1

The above figure is a picture of the coarse mesh to be used with problem 22.1.  The mesh contains 76 triangles, 56 linear nodes, and 188 quadratic nodes.  The first 56 nodes correspond to the linear (pressure elments).

The above is a picture of the medium mesh to be used with problem 22.1.  The mesh contains 308 triangles, 188 linear nodes, and 684 points, quadratic nodes.  As above, the first 188 points in the mesh correspond to the linear (pressure) nodes.

The fine mesh (not shown), contains 525 triangles, 303 linear nodes, and 1131 quadratic nodes.

The mesh is organized in three variables named point, theta, and boundary.  The point variable consists of x-y pairs organized in columns for each point in the mesh.  The theta matrix contains a colum for each element in the mesh and it provides the six indices one of each of the points in the element.  The boundary variable is a single row vector that maps each node in the mesh to a boundary.  For each point, the boundary arrray contains a zero (indicating an interior node), or a number between 1 and 8.  The top edge (y=1) is 1, the right edge (x=1.5) is 2, the bottom (y=0) is 3, the left edge (x=0) is 4, the top of the cylinder (y=.75) is 5, the right of the cylinder (x=1) is 6, the bottom of the cylinder (y=.25) is 7, and the left of the cylinder (x=.5) is 8.

The file theta2 has the periodic representation of the mesh included in it, i.e. it maps the nodes on the right boundary of the grid to the corresponding node on the left boundary.

Note: there is a file also in the course locker called "plotsolution.m"  This is a matlab .m file and may be used to plot the solution of the stokes flow problem.

### From Athena:

The files are located in the course locker. If you are logged onto Athena, the easiest way to get to them is to do the following:
```athena% add 2.274
athena% cp /mit/2.274/www/coarse_mesh.mat .
athena% cp /mit/2.274/www/medium_mesh.mat .
athena% cp /mit/2.274/www/fine_mesh.mat .
athean% cp /mit/2.274/www/drawmesh.m .```
The above should copy the data file coarse_mesh.mat, medium_mesh.mat, fine_mesh.mat, and the script file drawmesh.m into your local directory. See the instructions below for how to use these files from MATLAB.

### If you are using MATLAB:

Dowload the following files (see above):
1. coarse_mesh.mat
2. medium_mesh.mat
3. fine_mesh.mat
4. drawmesh.m
The first data file contains three arrays named point_coarse, theta_coarse, theta2_coarse, and boundary_coarse.  The second one contains variables named point_medium, theta_medium, theta2_medium, and boundary_medium. To load the variables into MATLAB put the above three files in the same directory and use the following commands:
```>>load coarse_mesh
>>drawmesh( point_coarse, theta_coarse );
`>>drawmesh( point_coarse, theta_coarse, boundary_coarse );`