One of the first steps in the finite element method (FEM) is splitting the domain on which the partial differential equation (PDE) is solved into small parts, called cells, which in sum make a mesh. FEniCS has always supported meshes consisting of simplex cells (e.g. triangles and tetrahedrons), but has limited support for meshes consisting of quadrilateral (quad) and hexahedral (hex) cells. Finite element problems solved on quad/hex meshes often have better approximation properties and better robustness to cell distortion than those solved on simplex meshes. The project idea aims at being able to assemble and solve the simplest PDE, a Poisson's equation, in 2D (quad mesh) and 3D (hex mesh) in FEniCS.

Organization

Student

Ivan Yashchuk

Mentors

  • Christopher Richardson
  • Jack S. Hale
  • Martin Aln├Žs
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2017