From 21de15a2e6563dae5da277685e193ee7e9cd93ef Mon Sep 17 00:00:00 2001 From: Mike Date: Fri, 31 Mar 2017 18:49:02 -0400 Subject: [PATCH] Fixed some of the typos in latex. --- Distributed_LDG_Method/LDGPoisson.cc | 2 +- Distributed_LDG_Method/README.md | 16 ++++++---------- 2 files changed, 7 insertions(+), 11 deletions(-) diff --git a/Distributed_LDG_Method/LDGPoisson.cc b/Distributed_LDG_Method/LDGPoisson.cc index cc0c1e4..6f7ee56 100644 --- a/Distributed_LDG_Method/LDGPoisson.cc +++ b/Distributed_LDG_Method/LDGPoisson.cc @@ -1454,7 +1454,7 @@ output_results() const // @sect4{run} // The only public function of this class is pretty much exactly // the same as all the other deal.ii examples except I setting -// the constant in the DG penalty ($\tilde{\sigma}}$) to be 1. +// the constant in the DG penalty ($\tilde{\sigma}$) to be 1. template void LDGPoissonProblem:: diff --git a/Distributed_LDG_Method/README.md b/Distributed_LDG_Method/README.md index 10f41a3..27eff22 100644 --- a/Distributed_LDG_Method/README.md +++ b/Distributed_LDG_Method/README.md @@ -62,11 +62,7 @@ the terminal from the main directory, The output of the code will be in .vtu and .pvtu format and be written to disk in parallel. The results can be viewed using -ParaView. The visualization of the -solution $u(x,y)$ from the results of the test case in this code can be -seen below. - -![u](image/poisson.png) +ParaView. ## Local Discontinuous Galerkin Method @@ -192,20 +188,20 @@ Find $u_{h} \in W_{h,k}$ and $\textbf{q}_{h} \in \textbf{W}_{h,k} $ such that, - \sum_{e} \left( \nabla w, \, \textbf{q}_{h} \right)_{\Omega_{e}} + -\langle \llbracket \, w \, \rrbracket \, , \, \widehat{\textbf{q}_{h} } +\langle \left[ \, w \, \right] \, , \, \widehat{\textbf{q}_{h} } \rangle_{\mathcal{E}_{h}^{i} } + -\langle \llbracket \, w \, \rrbracket \, , \, \widehat{\textbf{q}_{h} } +\langle \left[ \, w \, \right] \, , \, \widehat{\textbf{q}_{h} } \rangle_{\mathcal{E}_{D} \cup \mathcal{E}_{N}} \ &= \ \sum_{e} \left( w , \, f \right)_{\Omega_{e}} \\ \sum_{e} \left( \textbf{w} \, , \, \textbf{q}_{h} \right)_{\Omega_{e}} - \sum_{e} \left( \nabla \cdot \textbf{w} , \, u_{h} \right)_{\Omega_{e}} + -\langle \, \llbracket \, \textbf{w} \, \rrbracket \, , \, \widehat{u_{h}} +\langle \, \left[ \, \textbf{w} \, \right] \, , \, \widehat{u_{h}} \rangle_{\mathcal{E}_{h}^{i}} + -\langle \llbracket \, \textbf{w} \, \rrbracket \, , \, \widehat{u_{h}} +\langle \left[ \, \textbf{w} \, \right] \, , \, \widehat{u_{h}} \rangle_{\mathcal{E}_{D} \cup \mathcal{E}_{N}} \ &= \ 0 @@ -224,7 +220,7 @@ is, @f{align} \widehat{u_{h}} \; = \; \left\{ \begin{array}{cl} -\left\{ u_{h} \right\} \ + \ \boldsymbol \beta \cdot \left[ u_{h} \rrbracket & +\left\{ u_{h} \right\} \ + \ \boldsymbol \beta \cdot [ u_{h} ] \, & \ \text{in} \ \mathcal{E}_{h}^{i} \\ u_{h} & \ \text{in} \ \mathcal{E}_{N}\\ g_{D}(\textbf{x}) & \ \text{in} \ \mathcal{E}_{D} \\ -- 2.39.5