Types Of Finite Element Analysis Method

Generalized finite element method

This method includes functions may not be polynomials. Finite element analysis method is more effective to domains with problems such as boundaries, layered boundary and micro scale problem. Partition of unity unites these spaces and forms subspace.

hp Finite element analysis method

This is a generalized finite numerical method. It solves partial differential equations depending on the polynomial approximation. It includes variable size of element as h and polynomial degree as p. Babuska et al was the first to introduce hp FEM method. It is an exponential convergence method.

hpk Finite element analysis method

This method is same as hp FEM method which includes element variable size as h, approximation of polynomial degree as p and local approximation in exponential convergence in k-1 order.

Extended Finite element analysis method (XFEM)

It is also referred as partition of unity method (PUM), a first classical FEM. It was developed by Ted Belyschko and coworkers in 1999. It provides solution for discontinuous functions.

Spectral method

This method is widely used in applied mathematics and to solve partial differential equations. It provides solution for linear continuous function. This method is global approach.

Mesh free method

This method includes numerical solution algorithm to simulate physical phenomenon. It can be used in fluid dynamics and solid mechanics field. Geometry of meshfree method is similar to mesh or grid algorithm.

Discontinuous Galerkin method

This method solves partial differential equation problems. Reed and Hill was the first to introduce this method for hyperbolic neutron transport equation in the year 1973. High order equation can be easily solved with finite element and finite volume conceptual framework.

Questions:

• Describe DG method.
• What is the difference between mesh and mesh free method?
• What are generalized finite element analysis methods?