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# Tag Info

Accepted

### Stability of hyperbolic PDE and DG-FEM

Stability does indeed mean that small changes in the data lead to small changes in the solution. This can be shown for the linear advection equation through the energy method; in proving the stability ...
Accepted

### Intro to DG Finite Element methods

For parabolic/elliptic PDE's, I highly recommend Beatrice Riviere's book: Discontinuous Galerkin methods for solving elliptic and parabolic equations: theory and implementation. For hyperbolic PDE'...
• 12k
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### Library for generating Discontinuous Galerkin FEM mesh

You are confused about different concepts. A mesh is really just a collection of cells defined by the vertices of the mesh and which vertices together form each cell. Consequently, a mesh is an ...
• 55.7k
Accepted

### Does the weighted residual method not use energy minimization in any form?

The answer to your question depends on the problem. For example, consider the diffusion equation for a field $q$, with diffusivity $k$ and sources $f$. The variational form of this problem states that,...
• 10.3k

• 831
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### Spectral methods, Spectral Volume methods, Spectral Difference methods

"Spectral methods" usually means methods which make use of global basis functions. Fourier spectral methods use sine and cosine, and are used when you have periodic boundary conditions. Chebyshev ...
• 3,028

### Has a uniform estimate in k of the inf-sup constant for hp-DG methods for the Stokes problem been established?

The problem was solved recently: Lederer/SchÃ¶berl: Polynomial robust stability analysis for H(div)-conforming finite elements for the Stokes equations
• 1,124

### How to compute turbulent energy cascade

Of course, the Fourier transform is a linear operator. So, you have the kinetic energy defined as: $E(\mathbf{r}) = \frac{1}{2} \mathbf{u}(\mathbf{r}) \cdot \mathbf{u}(\mathbf{r})$. The Fourier ...

### Finite difference problem

Since this is apparently a homework problem, let's just illustrate the idea on a simple small example. Let's take the domain [0,1], with the discontinuity at $x=0.5$, and assume $\alpha$=1 to the left ...
• 2,545

### Interior penalty discontinuous Galerkin Matlab implementation

If you are adamant on using MATLAB, chapter 14 of the following book walks through a 2D IPDG Poisson problem using piecewise linear basis functions on triangles: The Finite Element Method: Theory, ...
• 607

• 3,028
Accepted

### Pros of Fourier-Galerkin spectral methods

Pros: With trigonometric basis functions your problem size is $N \text{log}(N)$ instead of $N^2$. Stabilization techniques are easy to implement and cheap: Filtering in the modal space. Zero padding ...
• 1,335