How can I specify PDE solution points using adaptmesh

I'm using the PDE toolbox to solve a basic elliptical problem. My particular case has a number of discrete points at which the solution u is specified. Since the basic PDE toolbox commands only seem set up to deal with Dirichlet boundary conditions along edges (i.e., not single points), I guess I need to implement these manually.

In my understanding, this is a fairly straightforward process using the FEM method. One merely specifies that the corresponding row of the stiffness matrix [K] is entirely 0, with the exception of a 1 at the index of the corresponding node. Then the value of that point is placed in the corresponding row of the solution (force) [F] matrix.

I know that one can use [K,M,F,Q,G,H,R] = assempde(___) to get the K and M matrices, and then implement the above modifications, then use u = assempde(K,M,F,Q,G,H,R) to obtain the new solution. But what are my options if I'm using the adaptive mesh solution process, [u,p,e,t] = adaptmesh(g,b,c,a,f), since it doesn't take these matrices as arguments?