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Tutorial 2
<br> <h1>The Finite Element Method and CMISS</h1> <p>This tutorial looks at basic finite element mesh creation in CMISS. This is discussed in Chapter 1 of the <a href="/documentation/course_notes/fembem_notes/" target="new">FEM/BEM Notes</a>.</p>
<h1>Refining a finite element mesh</h1>
<p>An important part of finite elements in practice involves refining an element mesh to give a new mesh on the same domain with an increased number of elements. This is covered in CMISS <a href="http://cmiss.bioeng.auckland.ac.nz/development/examples/1/11/113/index.html" target="new">example_113</a>. Refer to pages 20 and 21 of the <a href="/documentation/course_notes/fembem_notes/" target="new">FEM/BEM Notes</a>. When running this example you will make use of the 'fem_mesh.ip****' files that you created in example_111 in Tutorial 1. (Refer to Tutorial 1 for details on how to run a CMISS example or if you do not have the 'fem_mesh.ip****' files.)</p>
<h1>Defining a mesh with mixed basis functions</h1> <p>Refer to section 1.5 and page 20 of the <a href="/documentation/course_notes/fembem_notes/" target="new">FEM/BEM Notes</a>. To begin a new example the old example must be cleared. This is accomplished by restarting CMISS. A mixed basis element mesh is often desirable as it allows different interpolations to be used in different directions in the local element coordinates. Mixed order basis functions are covered in the CMISS <a href="http://cmiss.bioeng.auckland.ac.nz/development/examples/1/11/115/index.html" target="new">example_115</a>.</p>
<h1>Defining and changing a curved mesh</h1> <p>All the meshes and basis functions that you have created so far have not contained any derivative information at the nodes. Refer to section 1.6 of the <a href="/documentation/course_notes/fembem_notes/" target="new">FEM/BEM Notes</a>. Hermite basis functions contain derivatives and hence allow curved meshes. Run the CMISS <a href="http://cmiss.bioeng.auckland.ac.nz/development/examples/1/11/114/index.html" target="new">example_114</a>. This example consists of two parts. This first part defines a cubic Hermite - linear Lagrange mesh, and the second part lets you change the line slopes and nodal positions of the mesh you have created. This is done for the lines by changing the line control points (the '+' marker) by clicking and relocating and by clicking and relocating the node numbers for the nodes.</p>
<h1>Defining a triangular mesh</h1> <p>Triangular elements differ from the quadrilateral based meshes that you have already created in that they use area basis functions. These area basis functions are covered in section 1.7 of the <a href="/documentation/course_notes/fembem_notes/" target="new">FEM/BEM Notes</a>. Run the CMISS <a href="http://cmiss.bioeng.auckland.ac.nz/development/examples/1/11/116/index.html" target="new">example_116</a>.</p>
<hr> <p><b><a href="http://cmiss.bioeng.auckland.ac.nz/cgi-bin/lab-question-form.cgi?stage=1&laboratory=2" target="new">Tutorial 2 Quiz</a></b> | Tutorial 1 | Tutorial 3</p> <hr>