What is the advantage of Galerkin approach for finding the stiffness matrix?

It reduces the dimensionalilty of the problem hence it is much faster.

What makes Galerkin method so special?

Bubnov–Galerkin method (after Ivan Bubnov) does not require the bilinear form to be symmetric and substitutes the energy minimization with orthogonality constrains determined by the same basis functions that are used to approximate the solution.

What is the difference between Galerkin method and Rayleigh-Ritz method?

The Galerkin method, which is a weighted residual method, is in general applicable to differential and integral equations. In the Rayleigh-Ritz method, it is necessary that the co-ordinate functions satisfy only the kinematic boundary conditions.

Why do we need weighted residual method?

The weighted residual method is an efficient method to find the approximate solution of a differential equation. For a two-dimensional unsteady temperature field, the temperature must satisfy the differential equation of conduction of heat and the initial and boundary conditions.

Where is Galerkin method used?

The Petrov–Galerkin method is a mathematical method used to approximate solutions of partial differential equations which contain terms with odd order and where the test function and solution function belong to different function spaces.

What is weight function in Galerkin method?

A common approach, known as the Galerkin method, is to set the weight functions equal to the functions used to approximate the solution. That is, w i ( x ) = ϕ i ( x ) . (Galerkin) .

What is Rayleigh Ritz and Galerkin FEM analysis?

Finite-element methods (FEM) are based on some mathematical physics techniques and the most fundamental of them is the so-called Rayleigh-Ritz method which is used for the solution of boundary value problems.

What is the advantage of the FEM over finite difference FDM and finite volume Fvm methods?

The FVM is a natural choice for solving CFD issues because the PDEs you have to resolve for CFD are conservation laws. However, you can also use both FDM and FEM for CFD, as well. The FVM’s most significant advantage is that it only needs to do flux evaluation for the cell boundaries.

What is the difference between the residual method and weighted residual method?

While the collocation method enforces the residual to be zero at points, the method of weighted residuals requires weighted integrals of the residual to be zero. A weighted residual is simply the integral over the domain of the residual multiplied by a weight function, .

Which method of approach is useful for evaluating four noded quadratic elements?

Which method of approach is useful for evaluating four noded quadratic elements? Explanation: Gaussian quadrature is to select the n Gauss points and n weights such that provides an exact answer for polynomials f(ξ) of as large ∼ degree as possible.

What is the function of shape?

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions.