Symmetric finite volume discretizations for parabolic problems.
The paper deals with the following parabolic problem \[ \begin{aligned} u_t - \nabla (A \nabla u) + \alpha u = f, &\quad (x,t) \in \Omega \times (0,T],\tag{1}\\ u(x,0) = u_0(x), &\quad x \in \Omega,\tag{2}\\ u(x,t) = 0, &\quad (x,t) \in \partial \Omega \times (0,T],\tag{3} \end{aligned} \] where \(\Omega \subset R^2\) is a convex polygonal domain with boundary \(\partial \Omega\), \(u_0(x) \in L^2 (\Omega)\). The authors present and analyze one semi-discrete symmetric finite volume scheme and two full discrete symmetric finite volume schemes for (1)--(3). It is shown that these schemes preserve the symmetry of the original problem and also possess the advantages of the standard finite volume schemes. Adequate numerical examples are presented.
scientific article; zbMATH DE number 2031340
scientific article