What is a weak Galerkin?
Abstract. The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye in [29] for general second order elliptic problems on triangular meshes. The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.
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 Galerkin method of approximation?
In order to obtain a numerical solution to a differential equation using the Galerkin Finite Element Method (GFEM), the domain is subdivided into finite elements. The function is approximated by piecewise trial functions over each of these elements.
What is value of 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 ) = Ď• i ( x ) .
What is Galerkin approach used in FEM discuss its advantages?
Galerkin method is a kind of weighted residual method, where weight functions are same as basis/trial functions. Galerkin method is also popular in the finite element method (FEM) since it offers ease of implementation due to same weight and trial functions.
What is the meaning of weak formulation?
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain “test vectors” or “test functions”.
What is Galerkin weighted residual method?
In the method of weighted residuals, the next step is to determine appropriate weight functions. A common approach, known as the Galerkin method, is to set the weight functions equal to the functions used to approximate the solution.
What is the meaning of weak formulation Nptel?
What is the meaning of weak formulation? Solutions obtained are incorrect. The differentiability requirement on primary variable is decreased. The differentiability requirement on primary variable is increased. No Boundary conditions have to be satisfied.
What is CST and LST elements?
Why CST & LST is called constant & linear strain triangle element? CST – Constant Strain Triangle – First order Triangle Element – 3 nodes per Triangle. LST – Linear Strain Triangle – Second order Triangle Element – 6 nodes in Triangle. In CST – Strain in the element won’t vary.
What is a weak form?
Weak forms are syllable sounds that become unstressed in connected speech and are often then pronounced as a schwa. In the sentence below the first ‘do’ is a weak form and the second is stressed. Counting the number of words in a sentence, or sentence dictations can help raise awareness of weak forms.
Why is weak form important in FEM?
The weak form reduces the continuity requirements on the basis functions used for approximation which gives way to using lesser degree polynomials. This is done by converting the differential equation into an integral form which is usually easier to solve comparatively.