# Questions tagged [discontinuous-galerkin]

Questions about analysis, implementation or application of Galerkin methods for partial differential equations using piecewise functions that are not globally continuous (and hence require surface terms on element boundaries in addition to the usual volume terms occurring in finite element methods).

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### Gauss-Lobatto quadrature and nodal points for FEM

By using the Legendre-Gauss-Lobatto (LGL) quadrature formula (QF) and LGL nodal points one achives a diagonal mass-matrix for finite element problems. (More specifically, the spectral element method.) ...
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### Library for Discontinuous Galerkin method: FEniCS vs deal.ii

I am aware that both FEniCS and deal.ii are capable of solving problems with Discontinuous Galerkin (DG) method. I would like to specifically know if any of these two softwares can cater these ...
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### $L^\infty$ stability property of an ODE

Suppose we have the initial-value problem on $(0,L)$: $$\frac{d u(x)}{d x} = f(x) u(x),\, \qquad x\in\Omega,\,~~ u(0) = u_0,$$ I am reading a claim that says if we multiply the ODE by $u$ and ...
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### DG local equation, how to interpret mean-averaged test function

In the paper http://www.sciencedirect.com/science/article/pii/S0045782509003521, an HDG element-local equation is described on page 584 equation (4), with one of the equations taking the following ...
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### Viewing HDG FEM edge variables in vtk / paraview

For a 2D HDG code, I would like to be able to visualize the solution on the edge space between elements. Basically, this amounts to plotting the solution on the "green" nodes below. Is there a ...
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### Vandermonde matrix DG Hestaven

I am trying to understand the nodal and modal basis formulation from the book of Hesthaven (Nodal Discontinuous Galerkin Methods, Hesthaven, Jan S., Warburton, Tim). For $N=2$, I get the Vandermonde ...
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### Higher order interpolation in DWR method

Based on page $35$ of the book: (W. Bangerth and R. Rannacher, "Adaptive Finite Element Methods for Solving Differential Equations", Birkhäuser, 2003,) for computing the error in dual weighted ...
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### Orthonormal basis for hexahedron

Orthogonal polynomials are often preferred as basis functions. Recently I learned selecting orthonormal basis further simplifies the mass matrix from diagonal to simply the identity matrix when used ...
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### How do we implement Parameter free generalised Moment limiter in 1D Case in Discontinuous Galerkin methods?

I am referring to this paper:- "A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids " by Michael Yang and Z.J. Wang. http://dept.ku.edu/~cfdku/papers/AIAA-2009-...
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### Plot 2D piecewise constant in matlab in a finite elements mesh

I need to generate a discontinuous plot (piecewise in each triangle) in matlab, something like: This plot is from http://www.alecjacobson.com/weblog/?p=3616, but I don't understand how generate it. ...
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### CFL condition in Discontinuous Galerkin schemes

I have implemented an ADER-Discontinuous Galerkin scheme for the resolution of linear systems of conservation laws of the type of $\partial_t U + A \partial_x U + B \partial_y U=0$ and observed that ...
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### Numerical quadrature in Discontinuous Galerkin

I would like to know which is the best way to integrate numerically Legendre polynomials. I am building up a Discontinuous Galerkin CFD code for which Legendre polynomials are used as basis functions ...
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### Library for generating Discontinuous Galerkin FEM mesh

There are a number of packages available for generating Continuous Galerkin (CG) FEM meshes (gmsh, tetgen, netgen, etc.), but I have been unable to find one that generates Discontinuous Galerkin (DG) ...
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### Spectral methods, Spectral Volume methods, Spectral Difference methods

Could someone explain the link (if any) between the spectral methods (SM), as presented for example here and the so called spectral volume methods (SV) and spectral difference methods (SD) for CFD ? ...
I'd like to solve the elastodynamics equation for a problem with fast scales from an impact (although no shocks). $\rho\ddot{\mathbf{u}} - \nabla \cdot \sigma(\mathbf{u}) = \mathbf{f}$ In structural ...