FEM vs FVM vs FDM
The essential differences between these methods are illustrated in the figure.
💡 Using the FDM, the differential equation will be approximated using a different equation. This is a very easy method with an equidistant structured calculating mesh.
💡 The FEM approximates the solving space of the PDE, and the unknown function is interpolated by a set of basis functions that will help calculate the derivatives. It is more complex and has more flexibility decomposing the solution domain.
💡 The FVM starts with the integration of the PDE over a control volume. Using the divergence theorem, the integral over the volume will be substituted against an integral over the control volume's boundary. It is simpler than the FEM at first sight and still has the flexibility of arbitrarily decomposing the solution domain but with special volume decomposition requirements.
#fem #fvm #fdm
The essential differences between these methods are illustrated in the figure.
💡 Using the FDM, the differential equation will be approximated using a different equation. This is a very easy method with an equidistant structured calculating mesh.
💡 The FEM approximates the solving space of the PDE, and the unknown function is interpolated by a set of basis functions that will help calculate the derivatives. It is more complex and has more flexibility decomposing the solution domain.
💡 The FVM starts with the integration of the PDE over a control volume. Using the divergence theorem, the integral over the volume will be substituted against an integral over the control volume's boundary. It is simpler than the FEM at first sight and still has the flexibility of arbitrarily decomposing the solution domain but with special volume decomposition requirements.
#fem #fvm #fdm