2000 character limit reached
Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D (2011.12718v1)
Published 25 Nov 2020 in math.NA and cs.NA
Abstract: For a singularly perturbed elliptic model problem with two small parameters, we analyze finite element methods of any order on a Bakhvalov-type mesh. For convergence analysis, we construct a new interpolation by using the characteristics of layers. Besides, a more subtle analysis of the mesh scale near the exponential layer is carried out. Based on the interpolation and new analysis of the mesh scale, we prove the optimal convergence order.