The following use of NDSolve with time-dependent boundary conditions fails. There seems to be an uncompatibilty with the MethodOfLines Method since when I do not enforce it , no warning/errors are returned. Is there a way to fix this issue or shall I change of method ?

NDSolve[{D[c[x, y, t], t] -  Laplacian[c[x, y, t], {x, y}] == 
   NeumannValue[0, x >= t], 
  DirichletCondition[c[x, y, t] == 1, x <= t], 
  c[x, y, 0] == 0}, c, {x, 0, 100}, {y , -.5, .5}, {t, 0, 100}, 
 Method -> {"MethodOfLines", 
   "SpatialDiscretization" -> "FiniteElement"}]

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