<< NDSolve`FEM`
bm = ToBoundaryMesh[
   "Coordinates" -> {{0., 0.}, {1., 0.}, {2., 0.}, {2., 1.}, {1.,
      1.}, {0., 1.}},
   "BoundaryElements" -> {LineElement[{{1, 2}, {2, 3}, {3, 4}, {4,
        5}, {5, 6}, {6, 1}, {5, 2}}]}];
em = ToElementMesh[bm,
   "RegionMarker" -> {{{0.5, 0.5}, 1}, {{1.5, 0.5}, 2}}];

Show[{
  em["Wireframe"["MeshElementStyle" -> Directive[EdgeForm[Red], Thin],
     "MeshElementMarkerStyle" -> Blue]],
  bm["Wireframe"["MeshElementStyle" -> Black]]
  }, ImageSize -> 300]

sigma = If[ElementMarker == 1, 1, 2];
sl1 = NDSolveValue[{D[sigma*D[u[x, y], x], x] +
     D[sigma*D[u[x, y], y], y] == 0, DirichletCondition[u[x, y] == 0, x == 0],
   DirichletCondition[u[x, y] == 1, x == 2]}, u[x, y], {x, y} [Element] em]

Plot3D[sl1, {x, y} [Element] em, ColorFunction -> "Rainbow",
 PlotRange -> {0, 1}, ImageSize -> 300]

NIntegrate[
 Evaluate[sigma*(D[sl1, x]^2 + D[sl1, y]^2)], {x, y} [Element] em]

(* 0.667 *)

sigma*(D[sl1, x]^2 + D[sl1, y]^2) /. {x -> 0.5, y -> 0.5}

(* 0.444 If[ElementMarker == 1, 1, 2] *)

If[x < 1, 1, 2]*(D[sl1, x]^2 + D[sl1, y]^2) /. {x -> 0.5, y -> 0.5}
(*  0.444  *)

sl2 = NDSolveValue[{D[sigma*D[u[x, y], x], x] +
     D[sigma*D[u[x, y], y], y] == 0, jx[x, y] == sigma*D[u[x, y], x],
   jy[x, y] == sigma*D[u[x, y], y],
   DirichletCondition[u[x, y] == 0, x == 0],
   DirichletCondition[u[x, y] == 1, x == 2]}, {u[x, y], jx[x, y],
   jy[x, y]}, {x, y} [Element] em]

Plot3D[sl2[[1]], {x, y} [Element] em, ColorFunction -> "Rainbow",
 PlotRange -> {0, 1}, ImageSize -> 300]