Finite Element Method

• Continuous
  • The Poisson Problem
  • General Elliptic PDEs
  • Weak Formulation of the Poisson Problem
  • Example of Weak Solution to the Poisson Problem
  • Weak Formulation of Elliptic PDEs
• Discrete
  • The Discrete Formulation
  • From Basis to Shape Functions
  • Continuous Galerkin
• Reference domains
  • Reference Domains and Quadrature
  • 1D
    • The Line Domain
  • 2D
    • The Triangle Domain
    • The Quadrilateral Domain
  • 3D
    • The Tetrahedron Domain
    • The Hexahedron Domain
• Elements
  • Shape Functions on Reference Elements
  • 1D
    • The Line2 Element
    • The Line3 Element
  • 2D
    • The Tri3 Element
    • The Tri6 Element
    • The Quad4 Element
    • The Quad9 Element
  • 3D
    • The Tet4 Element
    • The Hex8 Element
• Meshes
  • Mesh Representation
  • Mesh Boundaries
  • MeshIO Interoperability
• Assembly
  • Computing the Jacobian
  • Bilinear Form Assembly
  • Load Vector Assembly
  • L² Projection
  • Dirichlet Boundary Conditions
  • Neumann Boundary Conditions