Fixed typo intro and updated references

diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib
index 771eebe869b069402555d46c7953bf68221d8df5..720e23acd4a3ec45039b0722064972cbe1cd2b3f 100644 (file)
--- 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 a84de5e0ca7f453228ee42a349f8fc1fb7a84aa6..41be66f388bba792400681dc3a7299ba156e9b20 100644 (file)
--- 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 <code>n_dofs = fe_values.dofs_per_cell</code> is the number of degrees of freedom per cell and <code>n_q_points = quad.size()</code> 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 <code>n_dofs = fe_values.dofs_per_cell</code> is the number of degrees of freedom per cell and <code>n_q_points = quad.size()</code> 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]