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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).
4
votes
1
answer
682
views
How to handle inflow and outflow boundaries for a non-linear convection-diffusion equation (...
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:
$$
\nabla\cdot(\mathbf{b …
3
votes
1
answer
440
views
Convergence of interior penalty DG methods
I’m currently having some issues with my routine for the linear advection-diffusion problem. The model problem is as follows:
$$
\nabla\cdot(\mathbf{s} u) - \nabla\cdot(\kappa\nabla u) = f, \;\;\;\tex …
14
votes
0
answers
542
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:
$$
-\nabla\cdot(D_{1}(u_{2},u …
6
votes
1
answer
804
views
How to project a vector into the H(div) space (in the context of finite elements)?
Say I have a simple elliptic PDE:
$$
-\nabla\cdot(K\nabla p) = f \;\;\;\text{in}\;\Omega
$$
with the appropriate boundary conditions. I solve for $p$ using a FEM (a discontinuous Galerkin method to b …
3
votes
2
answers
1k
views
Slow convergence of Newton's method for finite elements
The application is a simple non-linear advection diffusion problem (steady state) using DGFEM. My error at each iteration is given by
$$
e_{n+1} = ||\mathbf{J}^{-1}(\mathbf{u}_{n})\mathbf{F}(\mathbf{u …