Multiblock mixed finite element methods for singularly perturbed problems Original Research Article

A generic multiblock mixed finite element method is constructed for the singularly perturbed problem −ε2Δp+ap=f in the rectangle [0,1]2. The problem domain is decomposed into non-overlapping subdomains which separate the boundary layer subregions totally from other subregions. The global convergences of O(N−1), independent of ε for p and ε∇p in L2 -norm are obtained for the lowest Raviart–Thomas spaces on our specially designed piecewise rectangular mesh, where N is the number of divisions in each direction. Numerical results using an efficient domain decomposition algorithm are presented, which show that our special domain decomposition performs much better than a general decomposition. Some possible extensions and open problems are discussed.