This technique is known as the Double Envelopment or Pincer Movement.
A full pincer movement leads to the attacking army facing the enemy in
front, on both flanks, and in the rear. If attacking pincers link up
in the enemy's rear, the enemy is encircled. Such battles often end in
surrender or destruction of the enemy force, though the encircled
force can try to breakout. They can attack the encirclement from the
inside to escape, or a friendly external force can attack from the
outside to open an escape route.
This was the primary tactic used by Napoleon to break out the besieged forces under the command Marshal Saint-Cyr in Dresden.
Napoleon arrived quickly and unexpectedly with reinforcements to repel the assault by the larger Austrian, Russian, and Prussian combined force (Hereafter referred to as the Allied force).
After winning back initial defensive positions, Napoleon ordered his left French forces to drive back the allied right. The French right also quickly drove back the opposition forces and seized a critical bridge at Plauen, which severed the Allied left from the Allied center. The Allied center forces could do nothing but watch as their entire right flank was scattered, killed, or captured.
Napoleon had prepared for a continued day of fighting and made preparations but would not be given the chance. The allied forces opted to retreat during the night, despite holding a numerical superiority and a right flank anchor in Leubnitz that the French had yet to take during four full scale assaults.
At Austerlitz, Napoleon was hoping that the Allied forces would attack, and to encourage them, he deliberately weakened his right flank. Once he became satisfied at the weakness in the Allied enemy center as forces were diverted to the south, he launched his assault. The Allied forces were soon split in two and vigorously attacked and pursued both north and south of the plateau.
The primary difference is that at Austerlitz, Napoleon feigned a pincer in order to stretch the enemy forces, disguised the strength of his center, and provided swift reinforcements from outside the battlefield to his "weak" right flank. At Dresden, Napoleon realized that if he captured the bridge at Plauen, the Allied center had no way of changing position to meet the flank attack.