coordinate system - geotools / jts crs transformation result not at correct position

I copied the example from geotools, which shows how to transform a shapefile into a different projection. (http://docs.geotools.org/latest/userguide/tutorial/geometry/geometrycrs.html) But when transforming from Gauss Krueger 4 into Pseudo Mercator (3857) the shapes are not at the correct position, they are displaced several meters.

What can I do to fix this?

The sample code contains :

 CoordinateReferenceSystem dataCRS = schema.getCoordinateReferenceSystem();
            CoordinateReferenceSystem worldCRS = map.getCoordinateReferenceSystem();
            boolean lenient = true; // allow for some error due to different datums
            MathTransform transform = CRS.findMathTransform(dataCRS, worldCRS, lenient);

... and then ...

Geometry geometry2 = JTS.transform(geometry, transform);

additional information:

The sample data of the source as the following CRS

PROJCS["PD_83_3_degree_Gauss_Kruger_zone_4", 
  GEOGCS["GCS_PD/83", 
    DATUM["D_Potsdam_Datum_83", 
      SPHEROID["Bessel_1841", 6377397.155, 299.1528128]], 
    PRIMEM["Greenwich", 0.0], 

    UNIT["degree", 0.017453292519943295], 
    AXIS["Longitude", EAST], 
    AXIS["Latitude", NORTH]], 
  PROJECTION["Transverse_Mercator"], 
  PARAMETER["central_meridian", 12.0], 
  PARAMETER["latitude_of_origin", 0.0], 
  PARAMETER["scale_factor", 1.0], 
  PARAMETER["false_easting", 4500000.0], 
  PARAMETER["false_northing", 0.0], 
  UNIT["m", 1.0], 

  AXIS["x", EAST], 
  AXIS["y", NORTH]]

and the target has the following CRS:

PROJCS["WGS 84 / Pseudo-Mercator", 
  GEOGCS["WGS 84", 
    DATUM["World Geodetic System 1984", 
      SPHEROID["WGS 84", 6378137.0, 298.257223563, AUTHORITY["EPSG","7030"]], 
      AUTHORITY["EPSG","6326"]], 
    PRIMEM["Greenwich", 0.0, AUTHORITY["EPSG","8901"]], 

    UNIT["degree", 0.017453292519943295], 
    AXIS["Geodetic latitude", NORTH], 
    AXIS["Geodetic longitude", EAST], 
    AUTHORITY["EPSG","4326"]], 
  PROJECTION["Popular Visualisation Pseudo Mercator"], 
  PARAMETER["semi_minor", 6378137.0], 
  PARAMETER["latitude_of_origin", 0.0], 
  PARAMETER["central_meridian", 0.0], 
  PARAMETER["scale_factor", 1.0], 
  PARAMETER["false_easting", 0.0], 

  PARAMETER["false_northing", 0.0], 
  UNIT["m", 1.0], 
  AXIS["Easting", EAST], 
  AXIS["Northing", NORTH], 
  AUTHORITY["EPSG","3857"]]

Any idea? D3

Answer

Meanwhile I learned that I have to use the Bursa Wolf parameters for a precise transformation between shapes with different datum. The required parameters are in the Geotools hsql database, which can be 'queried' by CRS.decode().