Epoxy is best. The solid surface manufacturers sell color matched high strength epoxy for bonding, but a good epoxy works just as well. The surface should be sanded for best adhesion, and use the sanding dust to mix in the epoxy to color match it to the material. It helps disguise the seam.
Also, wipe the sanded surface that will be bonded with lacquer thinner before applying the epoxy.
We use this method on all of our solid surface materials and have never had a glue seam fail. The field material has cracked before the seam ever showed any stress fractures.
Epoxy is a bit flexible and has much higher shear strength than CA does.
