I am trying to solve $u\_{xx}+u\_{yy}=-[(3x+x^2)y(1-y)+(3y+y^2)x(1-x)] e^{x+y},$ for $0<x<1,0<y<1,$ and homogeneous Dirichlet boundary conditions $u(x,y)=x(1-x)y(1-y)e^{x+y}$ by an analytical method, a FEM method and NDSolve and then plot all solutions to a common graph. But for the analytical method I use:

```
NDSolveValue[{\!\(
\*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[x, 
 y]\)\) == [(3 x + x^2)*y*(y - 1) + (3 y + y^2)*x*(x - 1)]*
Exp[x + y], 
DirichletCondition[u[x, y] == x*(1 - x)*y*(1 - y)*Exp[x + y], 
True]}, u, {x, 
  y} \[Element] Disk[]]
Plot3D[%[x, y], {x, y} \[Element] Disk[]]

```

which doesn't work. I tried to make a FEM method, but it didn't work. For example, I tried for NDSolve`FEM`:

```
bndmesh = 
ToBoundaryMesh[
"Coordinates" -> {{0, 0}, {0.5, 0}, {0.5, 1}, {0, 1}, {1, 0}, {1, 
  1}}, "BoundaryElements" -> {LineElement[{{1, 2}, {2, 3}, {3, 
    4}, {4, 1}, {2, 5}, {5, 6}, {6, 3}, {3, 2}}]}];
mesh = ToElementMesh[bndmesh];
d = If[x <= 0.5, 1, 10];
usol = NDSolve[
Laplacian[
  u[x, y], {x, y}] == (3 x + x^2)*y*(y - 1) + (3 y + y^2)*
   x*(x - 1)*Exp[x + y], 
DirichletCondition[u[x, y] == x*(1 - x)*y*(1 - y)*Exp[x + y], 
  True] \[Element] mesh][[1]];
{bndmesh["Wireframe"], mesh["Wireframe"], 
Plot3D[u[x, y] /. usol, {x, y} \[Element] mesh]}

```