give (sb) satisfaction 使(某人)满意 (cf.2)
express one's satisfaction at [with] 对…表示满意
find satisfaction in doing 对做某事感到称心
His election was a great satisfaction to all concerned. 他的当选使大家都感到很满意
to sb's (entire) satisfaction 使某人(完全)满意地
to the satisfaction of 到…满意的程度;到…确信的程度.

demand satisfaction 要求赔偿;要求道歉[决斗]
give satisfaction 赔偿;答应决斗 (cf.1)
in satisfaction of 作为…赔偿
make satisfaction for 赔偿,偿还
take satisfaction 报仇.