# Tag Info

Accepted

### Motivation behind Collocation Method

I would not insist on demanding a geometrical meaning from Galerkin methods in general. There is a connection, but it becomes less meaningful as you extend it further and further. (In a sense, it ...
Accepted

### Don't we care about the numerical diffusion in the diffusion term?

We have the following problem: $$\frac{\partial u}{\partial t}+v\color{red}{\frac{\partial u}{\partial x}}-\nu\color{blue}{\frac{\partial^2u}{\partial x^2}}=0 \tag{*}$$ The function $u$ may represent ...
Accepted

### How do I integrate a function defined over an arbitrary area?

Instead of directly integrating over the area, it is often more convenient to use the divergence theorem to replace the area integral with an integral over the boundary edges. The divergence theorem ...

### Why do we have to resort to Higher order schemes for solving the 1-D advection equation/ continuity equation?

There is a difference between the requirements for a hyperbolic pde like $$u_t + a u_x = 0$$ and for a purely parabolic pde like $$u_t = u_{xx}$$ Suppose the solutions are smooth and you ...

### What is numerical damping in the context of time-dependent FEM solvers?

It is quite straightforward to demonstrate this for implicit Euler (aka backward Euler) on a scalar example. Consider the initial value problem $$\dot{y}(t) = i \alpha y(t), \ y(0) = 1$$ with solution ...