Indian Institute of Technology, Kanpur, India
March 22, 2010
Mesa Laboratory- Chapman Room
The Least-Squares Spectral Element Method (LSSEM)
For equations with self-adjoint and positive definite operators, the Galerkin formulation results in the same system of equations as in the Rayleigh-Ritz formulation. The Galerkin method does not exhibit the best approximation property. In practice, solution to convection dominated transport problems by the Galerkin method are often corrupted by spurious oscillations or wiggles. The classical Galerkin method also behaves poorly for high-speed compressible flows and shallow water wave problems. Notorious difficulties arise even for the solution of elliptic problems by the Galerkin mixed method. One example is incompressible, irrotational flow problems governed by the Laplace or Poisson equations of the potential.