X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/11f93a2e8880680f6b192298e5ce0697d2596a31..1874c46934f4ba7e8c2013d3829f65309456d292:/BookGPU/Chapters/chapter5/ch5.tex

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@@ -160,7 +160,7 @@ We refer the reader to Chapter \ref{ch7} for an example of a scientific applicat
 \subsection{Heat conduction equation}\index{heat conduction}
 First, we consider a two-dimensional heat conduction problem defined on a unit square. The heat conduction equation is a parabolic partial differential diffusion equation, including both spatial and temporal derivatives. It describes how the diffusion of heat in a medium changes with time. Diffusion equations are of great importance in many fields of sciences, e.g., fluid dynamics, where the fluid motion is uniquely described by the Navier-Stokes equations, which include a diffusive viscous term~\cite{ch5:chorin1993,ch5:Ferziger1996}.%, or in financial science where diffusive terms are present in the Black-Scholes equations for estimation of option price trends~\cite{}.
 
-The heat problem is an IVP \index{initial value problem}, it describes how the heat distribution evolves from a specified initial state. Together with homogeneous Dirichlet boundary conditions\index{boundary conditions}, the heat problem in the unit square is given as
+The heat problem is an IVP \index{initial value problem}, it describes how the heat distribution evolves from a specified initial state. Together with homogeneous Dirichlet boundary conditions\index{boundary condition}, the heat problem in the unit square is given as
 \begin{subequations}\begin{align}
 \frac{\partial u}{\partial t} - \kappa\nabla^2u =  0, & \qquad (x,y)\in \Omega([0,1]\times[0,1]),\quad t\geq 0, \label{ch5:eq:heateqdt}\\
 u =  0, & \qquad (x,y) \in \partial\Omega,\label{ch5:eq:heateqbc}