LAUSR

As ε goes to zero, the unique solution of the scalar advection‐diffusion equation ytε−εyxxε+Myxε=0 , (x,t)∈(0,1)×(0,T) with Dirichlet boundary conditions exhibits a boundary layer of size O(ε) and an internal layer of size O(ε) . If the time T is large enough, these thin layers, where the solution yε displays rapid variations, intersect and interact with each other. Using the method of matched asymptotic expansions, we show how we can construct an explicit approximation P˜ε of the solution yε satisfying ‖yε−P˜ε‖L∞(0,T;L2(0,1))=O(ε3/2) and ‖yε−P˜ε‖L2(0,T;H1(0,1))=O(ε) for all ε small enough.