From c48c278081b28997ba4a9da8a228859cfbd990b7 Mon Sep 17 00:00:00 2001 From: Diane Guignard Date: Thu, 23 Sep 2021 11:15:10 -0400 Subject: [PATCH] Fixed typo intro and updated references --- doc/doxygen/references.bib | 9 +++++---- examples/step-82/doc/intro.dox | 2 +- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib index 771eebe869..720e23acd4 100644 --- a/doc/doxygen/references.bib +++ b/doc/doxygen/references.bib @@ -1233,19 +1233,20 @@ @article{BGNY2020, title={{LDG} approximation of large deformations of prestrained plates}, author={A. Bonito and D. Guignard and R.H. Nochetto and S. Yang}, - journal={Submitted}, - year={2020}, - url = {https://arxiv.org/abs/2011.01086} + journal={To appear in Journal of Computational Physics}, + year={2021}, + url = {https://doi.org/10.1016/j.jcp.2021.110719} } @article{BGNY2021, - title={Numerical analysis of the LDG method for large deformations of prestrained plates}, + title={Numerical analysis of the {LDG} method for large deformations of prestrained plates}, author={A. Bonito and D. Guignard and R.H. Nochetto and S. Yang}, journal={Submitted}, year={2021}, url = {https://arxiv.org/abs/2106.13877} } + % ------------------------------------ % References used elsewhere % ------------------------------------ diff --git a/examples/step-82/doc/intro.dox b/examples/step-82/doc/intro.dox index a84de5e0ca..41be66f388 100644 --- a/examples/step-82/doc/intro.dox +++ b/examples/step-82/doc/intro.dox @@ -184,7 +184,7 @@ Furthermore, since we integrate on $K_c$, we only need to evaluate the discrete @f[ {\rm compute\_discrete\_hessians[i][q]}, \qquad 0\leq {\rm i} < {\rm n\_dofs}, \,\, 0\leq {\rm q} < {\rm n\_q\_points}, @f] -where n_dofs = fe_values.dofs_per_cell is the number of degrees of freedom per cell and n_q_points = quad.size() is the number of quadrature points on $K_c$. For any basis function $\varphi^n$ with support on a neighboring cell, the discrete Hessian $H_h(\varphi^n)$ evaluated on $K_c$ contains only the two lifting terms, but not the term involving $D^2)h\varphi^n$, since $\varphi^n|_{K}\equiv 0$. Moreover, only the lifting over the common face $e$ is nonzero on $K_c$, namely for all $x_q\in K_c$ +where n_dofs = fe_values.dofs_per_cell is the number of degrees of freedom per cell and n_q_points = quad.size() is the number of quadrature points on $K_c$. For any basis function $\varphi^n$ with support on a neighboring cell, the discrete Hessian $H_h(\varphi^n)$ evaluated on $K_c$ contains only the two lifting terms, but not the term involving $D^2_h\varphi^n$, since $\varphi^n|_{K}\equiv 0$. Moreover, only the lifting over the common face $e$ is nonzero on $K_c$, namely for all $x_q\in K_c$ @f[ H_h(\varphi^n)(x_q)=-r_e\left(\jump{\nabla_h\varphi^n}\right)(x_q)+b_e\left(\jump{\varphi^n}\right)(x_q). @f] -- 2.39.5