Variational based numerical solution of PDEs
by Yi Zhang
For problem , the variational type methods are based on the weak form
The numerical methods differs at the point of in which test function space is and in which function space the solution is searched.
1. Bubnov-Galerkin: test function space
- Finite element method: consists of splines with local support. Conforming FEM: , together with same bilinear form and linear form in discrete variational equation. Non-conforming FEM: or (similar for ) or both, which results in discrete variational eqution
- Spectral method: consists of orthogonal polynomials.