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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Projecting the initial state on a Discontinuous Galerkin basis
Context
I want to solve a 1D Burgers equation with a discontinuous Galerkin approach on the space-time domain $(x,t)\in [0,1]^2$. I want to project the function $u(x) = e^{-\frac{(x-0.5)^2}{0.02}}$ ...
- 37
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Boundary Conditions on the Inlet and Outlet in a Discontinuous Galerkin framework
In the book Discontinuous Galerkin Method (DGM), Analysis and Applications to Compressible Flow by Vít Dolejší and Miloslav Feistauer, Springer, it is mentionned, in section 8.3.2 that deals with ...
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Is AMG supposed to work with discontinuous Galerkin discretizations?
As the question says, are algebraic multigrid methods well suited to be used as preconditioners for problems discretised with Discontinuous Galerkin methods (say $p=1$)?
I've always used AMG (actually,...
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Discontinuous Galerkin for Stokes flow
Greetings fellow members,
I'm trying to implement a Discontinuous Galerkin scheme for a Stokes flow (Poiseuille). While I get very satisfactory results on the velocity, I'm suprised with negative ...
- 3
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Constructing metric terms for high order elements
Given 27 $(x,y,z)$ coordinates in 3D space which describe a generally curved quadratic hexahedron, which correspond to the HEXA_27 reference element figure with planar faces in $(\xi, \eta, \zeta)$ ...
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Galerkin projection in AMG
In the context of Classical AMG for elliptic problems discretised with finite elements (DG or CG), one has the (fine) matrix of the problem, say $A_0$, and the coarser operators of the hierarchy $\{...
- 405
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Intergrid transfer operator for Discontinuous Galerkin method (multigrid)
I am studying DG and I've seen that it's possible to define a multigrid method. Let's consider two nested grids $\Omega_{l-1}$ and $\Omega_{l}$ and $V_{l-1}$ and $V_l$ classical DG spaces, both of ...
- 405
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Iterative solver for high order DG methods (3D Laplace problem)
I have a 3D Laplace problem on quite a complicated geometry where I am using Discontinuous Galerkin method. My mesh is composed by hexas, hence I am employing classical tensor product basis functions $...
- 405
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280
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Finite difference problem
I have a problem to resolve with the Finite Difference method in $[a,b]$:
$$-\frac{d}{dx}(\alpha(x)\frac{du}{dx})= g(x),$$
with $\alpha(x) \in L^{\infty}$ continuous in $]a,c[$ and $]c,b[$ and ...
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Does the weighted residual method not use energy minimization in any form?
I've come across several texts/papers utilizing the concept of a minimum potential energy state corresponding to an equilibrium state, and I know that it is used in FEM formulations that are based on ...
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Discontinuous Galerkin for transport equation with non-constant advection
This question is mainly an inquiry about the usefulness of Discontinuous Galerkin (DG) for the time-independent transport equation of the form
$$\sigma u+\beta\cdot\nabla u =f,\;\;\;\text{on }\Omega\...
- 139
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Cell-based vs face-based finite element methods
Notation:
Denote $T_{h} = \left\{K\right\}$ to be a face-conforming triangulation of a domain $\Omega$ such that $K_{i} \cap K_{j} = \emptyset$ for $i \neq j.$ Additionally, denote $\mathcal{V}_{h} = ...
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solve a coupled PDE system with some discontinuity by a mixed FEM
$$
\begin{cases}
u_t=f(u,v,\nabla{v}),\\
\Delta{[g(u)v]}=0.
\end{cases}$$
I want to solve the above PDE system by a mixed FEM, that is, $u_t=f(u,v,\nabla{v})$ by discontinuous Galerkin (DG), where $f$...
- 317
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How can I solve this PDE system by discontinuous Galerkin method?
As is known to all, the discontinuous Galerkin method (DG) was first used to solve the equation $u_t+u_x=0$. Now I have the following system of PDEs:
$$
\begin{cases}
u_t=f(u,v,\nabla{v}),\\
\Delta{v}...
- 317
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Are both centered and upwind numerical fluxes correct in DGTD?
In discontinuous Galerkin time domain (DGTD) method, a critical concept is the numerical flux that is used to link neighbouring elements. The numerical flux is however not unique. The popular choices ...
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