# Creating a Simple 2-D Bilinear Lagrange Mesh

### Description

• This example creates, saves and refines a simple 2D, two-element mesh with Bilinear Lagrange finite elements.

### Basic Concepts

• After completing the Mesh module tutorials 1 and 2, you should understand that:
• Each node has one or more parameters associated with it, depending on the number of variables and the basis function type(s) chosen
• Elements are defined by specifying connections between nodes
• After completing this tutorial, you should understand:

• How to make and refine two-dimensional tensor-product finite element meshes
• Useful points to consider:
• In practice, we do not typically type in nodal coordinates for real meshes. We can import nodes and elements from a tab delimited xls file using the import/export/graph button in the node and element editors.

### Step-by-step Instructions

• The following instructions will guide you in creating the 2D mesh pictured below.

### Start Continuity

• Launch the Continuity Client
• Confirm that the mesh box under Use Modules: is checked

### Create Mesh

• Select rectangular Cartesian in the Global Coordinates: pop-up menu

• Click OK to submit Coordinate Form

• Choose Lagrange Basis Function→2D→Linear-Linear with 3 integration/collocation points for Xi 1, Xi 2, and Xi 3

• Click OK to submit Basis Form

• Confirm that Linear-Linear Lagrange 3*3 is already selected for you under Coordinate 1, Coordinate 2, and Coordinate 3

• Use the Insert Node button in the left panel to create 5 additional nodes for a total of 6

• In the Value fields next to Coordinate 1, Coordinate 2, and Coordinate 3 enter the following (X,Y,Z) nodal coordinates:

• Node 1: (0., 0., 0.)
• Node 2: (1., 0., 0.)
• Node 3: (2., 0., 0.)
• Node 4: (0., 1., 0.)
• Node 5: (1., 1., 0.)
• Node 6: (2., 1., 0.)
• Click OK to submit Node Form

• The element definition for element 1 is 1, 2, 4, 5, so enter this in the Global Node Numbers box

• Use the Insert Element button in the left panel to create another element

• The element definition for element 2 is 2, 3, 5, 6, so enter this in the Global Node Numbers box

• Click OK to submit Element Form

### Render the Mesh

• Click the lines radio button

• Click Render to display mesh

• Specify a filename to save the model in. The file will be saved as filename.cont6

### Refine the mesh four-fold and re-render

• Enter 4 for xi1, 4 for xi2, and 1 for xi3 under New Element per old element in

• Select the Local coordinates radio button under New nodal derivatives with respect to:

• Click OK to submit

• Click the lines radio button

• Click Render to display mesh. The result should look like the screenshot below.