# Tag Info

### Motivation behind Galerkin method

When I studied the finite element method in graduate school, this notion of multiplying by a weight function was also very alien to me. Eventually, I did find a nice (albeit non-rigorous) analogy ...
• 11.8k
Accepted

### How to robustly and numerically expand a $k$-order polynomial in two variables defined on a polygon domain?

The problem that you are seeing is a well known problem of these basis functions: $$\phi_{m,n}(x,y) = x^{m}y^{n}$$ I quote from here: The reason why the coefficient matrix is nearly singular and ...
Accepted

### Projection method FVM poisson part, adding source term

The smooth solution turned out to have BC's applied in the following way: Walls and inlet: $\frac{\partial p}{\partial n}=0$ Outlet: $p=0$ Actually thought that we need only one value of P to pin, not ...
• 316
Accepted

### Incompressible Navier-Stokes equations: Is projection method exact?

The projection scheme is indeed analytic, provided that the initial conditions are incompressible. You can derive it by taking the divergence of the evolution equation for $u$. Finding the ...
• 159