Transient darcy flow equation

Question

I can solve the following stationary Darcy problem:

$div(\nabla u)=1$ with $ u = 0 \in \Gamma_d$

<< NDSolve`FEM`
x0 = 40;
y0 = 30;
r = 30;
p = Polygon[{{0, 0}, {75, 0}, {75, 30}, {45, 30}, {35, 40}, {0, 
     40}}];
m = ToElementMesh[p, "MeshOrder" -> 1, MaxCellMeasure -> 10 ];
usol = NDSolve[{ Laplacian[u[ x, y], {x, y}] == 1, 
    DirichletCondition[u[x, y] == 0, True] }, 
   u, {x, y} \[Element] m];
ContourPlot[Evaluate[u[ x, y] /. usol], {x, y} \[Element] m, 
 ColorFunction -> "Temperature", AspectRatio -> Automatic]

But I can't solve the following transient problem

$\frac{\partial u}{\partial t} + div(\nabla u)=t$ with $ u = 0 \in \Gamma_d$

usol = NDSolve[{D[u[t, x, y], t] - Laplacian[u[t, x, y], {x, y}] == t,
     DirichletCondition[u[t, x, 0] == 0, True], u[0, x, y] == 0}, 
   u, {t, 0, 1}, {x, y} \[Element] m];
ContourPlot[Evaluate[u[0.1, x, y] /. usol], {x, y} \[Element] m, 
 ColorFunction -> "Temperature", AspectRatio -> Automatic]

Can anyone help?

Answer 1

I solved like this:

<< NDSolve`FEM`
x0 = 40;
y0 = 30;
r = 30;
p = Polygon[{{0, 0}, {75, 0}, {75, 30}, {45, 30}, {35, 40}, {0, 
     40}}];
m = ToElementMesh[p, "MeshOrder" -> 1, MaxCellMeasure -> 1];
op = (D[u[t, x, y], t] - Laplacian[u[t, x, y], {x, y}]) - 1
(*ic={u[0,x,y]\[Equal]Evaluate[u[x,y]/.usol]};*)

ic = {u[0, x, y] == 0};
sol = NDSolveValue[{op == 0, 
   DirichletCondition[u[0, x, y] == 0, True], ic}, 
  u, {x, y} \[Element] m, {t, 0, 1000}]
Manipulate[
 ContourPlot[Evaluate[sol[t, x, y]], {x, y} \[Element] m, 
  ColorFunction -> "Temperature", AspectRatio -> Automatic, 
  PlotRange -> All], {t, 0, 1000, 1}]