# Tag Info

Accepted

### Flux sign and face normal confusion in finite volume method

When dealing with conservation laws like your case, you can often make use of the divergence theorem (as you did). You can then express the fact that the total mass within your integration region is ...
• 1,976
Accepted

### Solving geodesics on triangular meshes gives negative distances

The solution to the final Poisson equation is defined only up to an additive constant. So you just need to shift the solution vector so the smallest value is zero.
• 156

### Two-dimensional heat equation with Neumann boundary conditions: any hope to find an analytical solution?

Expanding (sort of) on @MPIchael's answer, you can pick any smooth function you like and plug it into the heat equation to give a problem to then work the other way. In numerical methods, we call this ...
• 10.8k
Accepted

### Lumped matrices in thermal analysis using finite elements

No, you can't lump the $K$ matrix: that would not be a consistent approximation to the second-order differential operator it is supposed to represent. But if you're trying to be a bit more formal, ...
• 50.7k

### (FEM) 1D time-dependent heat equation convergence problem

From the comments, I believe you are struggling with the FEM formulations and therefore fail to see what happens if the diffusion coefficient tends to zero. I don't have access to your book, but I ...
• 172

### Finite Difference Grid Spacing and Scaling

Let's assume the following heat transient heat transfer equation in 1D : $$\frac{\partial T} {\partial t} = \alpha \frac{\partial^2 T}{\partial x^2}$$ If we take its finite difference ...
• 1,127

### Simulating the heat equation with insulating material

Why even bother to simulate the left half? Why not just simulate the right half with the left BC being the constant value? Seems simpler and more accurate to what you want to actually model, because ...
• 1,902

• 1,606
1 vote

### Computing geodesic distances with diffusion

Combinatorial Laplacian ? It depends on what you expect from your solution. Something reasonable to expect is that your solution should be independent of the way you mesh your surface (or as ...
• 2,185
1 vote

### Solving the diffusion/heat equation for a randomly distributed set of points in 3D

If you have a cloud of points and you don't want to use mesh-based methods like FEM or FVM, a possibility is to use a mesh-free method like the Finite Point Method. For instance, you could have a look ...
1 vote

### V-cycle Multigrid for 2D transient heat transfer on a square plate using finite difference

Regarding your issue of multigrid taking longer than Gauss-Seidel: It could be that you didn't code the interpolation/restriction operations very efficiently. Do you make sure to take full advantage ...
• 158

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