Elliptic1D Add Scalar Boundary Conditions

Solves the 1D Poisson equation with Robin boundary conditions. This is the exact same problem as elliptic1D.jl, with addScalarBC used instead of robinBC. The equation to solve is

\[\nabla^2 u(x) = f(x)\]

with $x \in [0, 1]$ and $f(x) = e^x$. The boundary conditions are given by

\[a u + b \frac{du}{dx} = g\]

with $a = 1$, $b = 1$, and

\[a u(0) + b \frac{du(0)}{dx} = 0\]

\[a u(1) + b \frac{du(1)}{dx} = 2 e\]

This corresponds to the call to addScalarBC! of addScalarBC!(A, b, k, m, dx, bc), where bc is a boundary condition struct that contains the tuples dc, nc, and v which hold the coefficients for $a$, $b$, and $g$ in the above systems of equations. dc $= (1.0, 1.0)$, nc $= (1.0, 1.0)$, and v $= (0.0, 2.0 * \exp(1))$.

The key difference is the implementaiton of the boundary condition operators. In elliptic1D.jl, the right hand side of the Robin operator is included in lines 30-32, yet in this example, the boundary conditions are set via the addScalarBC! operator.

The true solution is

\[u(x) = e^x\]

This example is implemented in elliptic1DaddScalarBC.jl