Discontinuous Galerkin time stepping combined with spatial mixed finite element method for a time-dependent fourth-order singularly perturbed problem in 2D

In this paper, a fully discrete scheme is devised for solving a time-dependent singularly perturbed problem. The approach integrates a discontinuous Galerkin method for temporal discretization with a mixed finite element method for spatial discretization. To achieve parameter-robust convergence, we employ the original Bakhvalov mesh to discretize the spatial domain. Furthermore, based on supercloseness estimates, we eliminate the influence of some error terms and derive an optimal-order parameter-uniform convergence rate under the L 2 -norm for our numerical method, considering the mesh’s unique features. This is the first proof of this kind in the research literature, the error estimates having only been established so far in the energy-norm for the fourth-order singularly perturbed problem. Numerical experiments confirm the theoretical findings.