Error estimate of the cell-centered nonlinear positivity-preserving two-point flux approximation schemes

Abstract

We present the error estimate of nonlinear positivity-preserving finite volume schemes for diffusion problems. These schemes are also named by nonlinear two-point flux approximation (NTPFA) methods. Due to their conservation and monotonicity, such schemes have attracted wide attention. Under suitable regularity assumptions on the exact solution, we prove a discrete H1 error estimate through the analysis of consistent errors. Some numerical examples are presented to demonstrate the theoretical results.