History for Tutorial 2

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<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>

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<p><b><a href="http://cmiss.bioeng.auckland.ac.nz/cgi-bin/lab-question-form.cgi?stage=1&amp;laboratory=2" target="new">Tutorial 2 Quiz</a></b> | [Tutorial 1] | [Tutorial 3]</p>
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