A generalized collage method based upon the Lax–Milgram functional for solving boundary value inverse problems Original Research Article

Some inverse problems can be cast as approximating a given target function (perhaps the interpolation of observational data points) by the fixed points of an operator equation. The “collage method” refers to the solution strategy of bounding above the true approximation error by a more readily minimizable quantity. In this paper, we present a collage method for solving inverse problems for boundary value problems. The approach is based upon the Lax–Milgram representation theorem. For applications, we focus on one- and two-dimensional steady-state reaction–diffusion equations.