The finite difference streamline diffusion methods for Sobolev equations with convection-dominated term
Consider the linear Sobolev equation \[ \begin{multlined} c(x,t){\partial u\over\partial t}+ d(x,t)\cdot\nabla u-\nabla\cdot \Biggl[a(x, t)\nabla u+ b(x,t) \nabla{\partial u\over\partial t}\Biggr]+ \sigma(x, t) u=\\ f(x, t),\qquad (x,t)\in \Omega\times (0,T]\end{multlined} \] with the boundary and initial conditions \[ u(x, t)= 0,\quad (x, t)\in\partial\Omega\times [0,T],\quad u(x,0)= u_0(x),\quad x\in\Omega,\quad t= 0,\quad\Omega\subset \mathbb{R}^2, \] with some smoothness and positivity conditions on the coefficients. The purpose of the present paper is to derive two ``finite difference streamline diffusion schemes'', to study their stability and give error estimates in suitable norms.
finite difference streamline diffusion schemes
scientific article; zbMATH DE number 1861000
scientific article