# 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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### $L^\infty$ 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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### 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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### Explicit DG time step restriction for compressible Navier-Stokes equations

Hesthaven's book 1 mentions the following time step restriction for Navier-Stokes equations (see (7.32) in 2008 edition) $$\Delta t \approx \frac{h}{N^2} \frac{C}{|u| + |c| + \frac {N^2 \mu}{h}}$$ (\$...
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### Solution predictors for accelerating convergence in nonlinear FEM

I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static ...
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I am going through the book of Hesthaven and Warburton on discontinuous Galerkin methods. I have difficulties understanding some basic steps in the calculations. Consider the PDE: $$\frac{\partial u}... 0answers 475 views ### Library for Discontinuous Galerkin method: FEniCS vs deal.ii I am aware that both FEniCS and deal.ii are capable of solving problems with Discontinuous Galerkin (DG) method. I would like to specifically know if any of these two softwares can cater these ... 1answer 197 views ### Normalization of polynomials for discontinuous Galerkin methods (DGM) I was curious if someone could share their opinion on this matter. I have noticed that some people in literature normalize their Legendre polynomials, i.e. divide or multiply the polynomial by$$\...
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There are two general approaches to representing solutions in the discontinuous galerkin method: nodal and modal. Modal: Solutions are represented by sums of modal coefficients multiplied by a set of ...