I built a model to simulate the spread of a phenomenon in France from Paris. I use FEM. But I do not know what Dirichet or Newman boundary conditions I must apply. My small program. Do you have a solution? André Dauphiné
ClearAll["Global`*"]
Needs["NDSolve`FEM`"]
carto = DiscretizeGraphics[
CountryData["France", {"Polygon", "Mercator"}]];
bmesh = ToBoundaryMesh[carto, "MaxBoundaryCellMeasure" -> 25,
AccuracyGoal -> 1];
mesh = ToElementMesh[bmesh, MaxCellMeasure -> 5,
"MaxBoundaryCellMeasure" -> 25]
mesh["Wireframe"]
op = \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(u[t, x, y]\)\) -
Inactive[Laplacian][u[t, x, y], {x, y}] - 20;
dc = DirichletCondition[u[t, x, y] == 0, x == 0 && 8 <= y <= 10];
nc = NeumannValue[-2*u[t, x, y], (-5 + x)^2 + (-5 + y)^2 == 9];
uifHeat =
NDSolveValue[{op == nc, dc, u[0, x, y] == 0},
u, {t, 0, 100}, {x, y} \[Element] mesh];
Show[ContourPlot[uifHeat[x, y], {x, y} \[Element] mesh,
ColorFunction -> "Temperature"], bmesh["Wireframe"]]