A partial differential equation
\[
\frac{\partial^{2} T}{\partial x^{2}}+\frac{\partial^{2} T}{\partial y^{2}}=0
\]
is defined for the two-dimensional field $T: T(x, y)$, inside a planar square domain of size $2 \mathrm{~m} \times 2 \mathrm{~m}$. Three boundary edges of the square domain are maintained at value $T=50$, whereas the fourth boundary edge is maintained at $T=100$.
The value of $T$ at the center of the domain is
- $50.0$
- $62.5$
- $75.0$
- $87.5$