Finite element method on a Bakhvalov-type mesh for a singularly perturbed problem with two parameters
share
We reconsider a linear finite element method on a Bakhvalov-type mesh for a singularly perturbed problem with two parameters, which has been discussed in Brdar and Zarin (J. Comput. Appl. Math., 292 (2016), pp. 307–319). A novel interpolant is introduced for convergence analysis. From this interpolation, error analysis with Lagrange interpolation on the Bakhvalov-type mesh becomes feasible. As a result, we not only prove an optimal convergence between the true solution and the numerical solution, but also get a supercloseness result between the Lagrange interpolant and the numerical solution. More importantly, our arguments can be easily generalized to more general situations.
READ FULL TEXT