  We construct a finite element like scheme for fully non-linear
integro-partial differential equations arising in optimal control of
jump-processes. Special cases of these equations include optimal portfolio and
option pricing equations in Finance. The schemes are monotone and robust. We
prove that they converge in very general situations, including degenerate
equations, multiple dimensions, relatively low regularity of the data, and for
most (if not all) types of jump-models used in Finance. In all cases we provide
(probably optimal) error bounds. These bounds apply when grids are unstructured
and integral terms are very singular, two features that are new or highly
unusual in this setting.
