We present a finite element approximation which is effective for diffusion problems with dominated non-linear convection terms. This approximation is conservative and of upwind type. We analyse it in connection with L2 -theory, L1 -contraction and monotonicity. As an application we consider a non-linear elliptic problem and give error analysis. In the process the existence of the exact solution is also proved.
ASJC Scopus subject areas
- 数学 (全般)