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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

### 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
Accepted

### Discontinuous Galerkin for Stokes flow

In the Stokes equations, there is no "physically reasonable" pressure. The pressure is only defined up to an additive constant. Every pressure you move up or down by a constant is physically ...
• 55.7k

### Constructing metric terms for high order elements

Let's assume you have a way of computing the 27 tri-quadratic shape functions associated with the 27 points (either by tabulating them as polynomials, or by computing them as interpolating Lagrange ...
• 55.7k

### Intergrid transfer operator for Discontinuous Galerkin method (multigrid)

There is really nothing different between continuous and discontinuous finite element spaces: The injection mapping you state is exact in the sense that you can represent a coarse function on the fine ...
• 55.7k
Accepted

### Galerkin projection in AMG

Sorry, I have been busy lately. I don't have enough time to write the answer I want to, however, here is the short one: In GMG you define the prolongation and restriction operators based on the finite ...
• 2,751
1 vote
Accepted

### Iterative solver for high order DG methods (3D Laplace problem)

The canonical way to solve high-order problems efficiently is to use a multigrid method in which the first coarsening steps reduce the polynomial degree by one in each step, followed by (geometric) ...
• 55.7k
1 vote

### Discontinuous Galerkin for transport equation with non-constant advection

If the exact solution of the transport problem is not smooth, the numerical solutions using the continuous finite element method may exhibit spurious oscillations around the discontinuity. As you said,...

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