create PDEcs class for PDE constrained solver.

This example is a toy model for reconstruction of coefficient of PDE, though it is only 1 dimensional, however, evaluating gradient will be more or less O(n) complexity for a normal case. And it will be very slow in many cases.

For corase mesh, sometimes it cannot find the optimal since the problem maybe not convex or search direction is not good enough.
Remove linear interpolation from Assembler.

It is too specific. Remove for consistency of other codes.

Signed-off-by: Yimin <zhongym8903@gmail.com>
Add regularization to the test case.

It is very easy to prove the uniqueness for this simple case, however, the problem is
not very good, since it is EIT problem related, statbility is  very bad, and regularization is almost always needed.

without regularization coefficient beta, the algorithm will stop very early and cannot proceed. A very tiny beta will push it forward.