Tagged Questions

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).

34 views

Time integration for elastodynamics

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 ...
29 views

FEM libraries with trace spaces

To implement hybridizable discontinuous Galerkin methods, one needs finite element spaces defined on the skeleton of the mesh. deal.II has support for HDG through FE_FaceQ class which provides ...
15 views

Traction vector term in Discontinuous galerkin weak formulation

So I was working on Discontinuous Galerkin method and have been stuck up with this problem. This is a term in my weak form: where 't'= traction on the surface, 'w'=test function, 'n'=unit normal to ...
91 views

Role of the numerical flux in DG-FEM

I am learning the theory behind DG-FEM methods using the Hesthaven/Warburton book and I am a bit confused about the role of the 'numerical flux.' I apologize if this is a basic question, but I have ...
43 views

268 views

Matlab implementation of 2D Interior penalty discontinuous Galerkin poisson problem

Basically, I am trying to solve the 2D poisson problem in order to learn implementation of IPDG methods. The problem states $-\nabla a(x)(\nabla u)=0\ \text{in} \ \Omega$ with $U=0$ on Dirichlet ...
233 views

What's the difference between C0 penalty methods and Discontinuous Galerkin methods?

I am trying to understand the DG FEM methods, but I got lost in their definitions. In some papers I read that the "C0 penalty method" is one example of the DG method, but sometimes they are separated ...
174 views

163 views

How to prove the strong formulation for Discontinuous Galerkin is conservative?

I've been trying to figure out how to prove that the following equation is conservative $$\int_{D^k} \partial_t(u^k) v_j^k + \partial_x(f) v_j^k dx = [(f -f^*) v^k_j]_{x^k}^{x^{k+1}}$$ where $v_j^k$ ...
103 views

Discontinuous Galerkin energy method

I am studying DG for conservation laws from this book. Local inner product is defined like $$(u,v)_{D^k} = \int_{D^k} uv dx$$ and the $L^2(D^k)$-norm as (u,u)_{D^k} = ||u||^2_{...
134 views

Problem with implementing linear advection using DG-method

I am trying to implement a second order DG-method using a monomial basis and explicit Euler in time. I have written down some of the theory, which I present below: Theory Consider the linear ...
200 views

Are additional penalty terms necessary to solve elliptic PDE's with DG-FEM?

After a cursory glance at several references to discontinuous galerkin finite element methods for the elliptic poisson PDE, i notice that all of them emphasize using penalty methods where an ...
78 views

Mixed DG for Poisson with mixed BC's

I am trying to find a good reference on a proper weak formulation for mixed DG (Raviart Thomas and DG) formulation for a Poisson equation with mixed boundary conditions. Can anyone suggest a good ...
140 views

Optimal Discontinuous Galerkin (DG) solver on a parallel system

I am seeking the optimal method for implementing DG on a parallel system. For my research, I come across two types of problems. For the first problem, I am solving a time-independent (steady-state) ...
161 views

Evaluation of interface terms in Discontinuous Galerkin method

I would like to ask how is the evaluation of integrals over inter-element interfaces implemented in a typical DG code. I can think of two basic approaches (I assume 2D mesh here): 1) Perform 1D ...
320 views

Recommendations on FEM software for implementing Nitsche's method on interfaces between matching meshes?

Suppose: I have two domains, $\Omega_{1} = [0, 1/2] \times [0, 1]$ and $\Omega_{2} = [1/2, 1] \times [0, 1]$. The domains share an interface \$\Gamma = \{1/2\} \times [0, 1] = \partial\Omega_{1} \cap ...
457 views

Which finite-element framework allows the easy implementation of HDG methods?

I have tinkered around with the implementation of hybridizable Discontinuous Galerkin (HDG) methods in DUNE-PDELab and DUNE-FEM for my PhD but since then I have not had the time to work on these codes ...
182 views

Nodal DG method and limiters for hyperbolic conservation laws

All the papers I have seen on DG methods for hyperbolic conservation laws together with limiters to compute discontinuous solutions make use of Taylor polynomial basis (Pk basis) or Legendre ...
379 views

Is discontinuous Galerkin really any more parallelizable than continuous Galerkin?

I've always heard that easy parallelization was one of the advantages of DG methods, but I don't really see why any of those reasons don't also apply to continuous Galerkin.
291 views

Following "A conservative DGM for Convection-Diffusion and Navier-Stokes Problems" (Oden and Baumann), if we have a linear convection-diffusion equation of the following form: $$\nabla\cdot(\mathbf{b}... 0answers 189 views Sequential approach to solving coupled PDEs I'm dealing with a coupled system of three transient, non-linear convection-diffusion equations. Let's just say to simplify the problem that they take the following form:$$ -\nabla\cdot(D_{1}(u_{2},...
117 views

Quadrature-free DG method using nodal Lagrangian basis are computationally very efficient. I have seen many papers using this method for linear PDE but almost no literature for non-linear PDE like ...
397 views

The application is a simple non-linear advection diffusion problem (steady state) using DGFEM. My error at each iteration is given by $$e_{n+1} = ||\mathbf{J}^{-1}(\mathbf{u}_{n})\mathbf{F}(\mathbf{u}... 1answer 222 views Convergence of interior penalty DG methods I’m currently having some issues with my routine for the linear advection-diffusion problem. The model problem is as follows:$$ \nabla\cdot(\mathbf{s} u) - \nabla\cdot(\kappa\nabla u) = f, \;\;\;\...
1k views

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 ...
262 views

Local inversion of small matrices on GPUs?

I don't know much about GPU computing at the moment, so please pardon the simple question. Can one invert local matrices in parallel on the GPU? CUBLAS doesn't seem to support factorization, and most ...