Australian Mathematical Society
A new preconditioning-based parameter-uniform convergence analysis is presented for one-dimensional singularly perturbed convection-diffusion problems discretized by an upwind difference scheme on a Bakhvalov-type mesh. The proof technique utilizes the classical convergence principle: uniform stability and uniform consistency imply uniform convergence, which can only be used after applying an appropriate preconditioner to the discrete operator.
Nhan, T., & Mai, V. (2020). A preconditioning-based analysis for a Bakhvalov-type mesh. ANZIAM Journal, 62, C146–C162. https://doi.org/10.21914/anziamj.v62.16093