Usually, the smoothness of solutions in the interior domain is higher, and the smoothness near the boundary is lower. One natural combination is to choose high order Lagrange-FEM in the interior subdomain, and lower order Lagrange-FEM in the boundary layer. This chapter displays the significance of combinations to solve not only the singularity problems but also the general elliptic equations. Also, such a combination of various FEMs is also a representative for many other kinds of combined methods using different admissible functions. The k— order Lagrange FEM can be used on the solution domain S if the solution u ∈ H k +1(S). However we have to use the linear finite element method on S if u ∈ H2(S) only. The smoothness of the solutions of elliptic equations is, generally, different on different subdomains. For example, the solution u satisfies (Figure 5.1): $$ u \in {{H}^{2}}\left( S \right),u \notin {{H}^{3}}\left( S \right)andu \in {{H}^{{k + 1}}}\left( {{{S}_{2}}} \right)\left( {k \geq 2} \right), $$ where S consists of two subdomains, S1 and S2. Since u ∈ H2(S) only, the linear FEM has to be used on S1 with relatively small linear elements. Clearly, the k-order Lagrange FEM ought to be used on S2 because u ∈ H k +1(S2) (k ≥ 2). We hope that relatively large, k-order elements are applied in S2 such that calculation work and storage space can be saved.