diff --git a/web/content/docs/benchmarks/heatconduction/heatconduction-dirichlet.pandoc b/web/content/docs/benchmarks/heatconduction/heatconduction-dirichlet.pandoc index ef514b8eaffd69816829a75c4d1124eb7c033fe2..8617c578fb392ee6b692da6b60793f08bd4a9656 100644 --- a/web/content/docs/benchmarks/heatconduction/heatconduction-dirichlet.pandoc +++ b/web/content/docs/benchmarks/heatconduction/heatconduction-dirichlet.pandoc @@ -24,19 +24,19 @@ w.r.t boundary conditions $$ \eqalign{ T(x) = g_D(x) &\quad \text{on }\Gamma_D,\cr -k{\partial T(x) \over \partial n} = g_N(x) &\quad \text{on }\Gamma_N, +\lambda {\partial T(x) \over \partial n} = g_N(x) &\quad \text{on }\Gamma_N, } $$ where $T$ could be temperature, the subscripts $D$ and $N$ denote the Dirichlet- and Neumann-type boundary conditions, $n$ is the normal vector pointing outside of $\Omega$, and $\Gamma = \Gamma_D \cup \Gamma_N$ and $\Gamma_D \cap \Gamma_N = \emptyset$. ## Problem specification and analytical solution -We solve the Parabolic equation on a line domain $[60\times 1]$ with $k = 3.2$ and $\rho C_\textrm{p} = 2.5e10^6$ w.r.t. the specific boundary conditions: +We solve the Parabolic equation on a line domain $[60\times 1]$ with $\lambda = 3.2$ and $\rho C_\textrm{p} = 2.5e10^6$ w.r.t. the specific boundary conditions: $$ \eqalign{ T(x) = 274.15 &\quad \text{on } (x=0) \subset \Gamma_D,\cr -k {\partial T(x) \over \partial n} = 0 &\quad \text{on } (x=60) \subset \Gamma_N. +\lambda {\partial T(x) \over \partial n} = 0 &\quad \text{on } (x=60) \subset \Gamma_N. } $$