Wikipedia
Flexpde
FlexPDE is a general-purpose software for obtaining numerical solutions to partial differential equations in 2 or 3 dimensions. It is based on the Finite Element Method.
FlexPDE can solve steady-state or time-dependent problems; eigenvalue analysis; and free boundary problems. Moreover FlexPDE can be used in combination with CheFEM.
FlexPDE It is a commercial package; however a free student package is available that can solve many practical problems. The student version is restricted in meshsize and the number of variables allowed, but otherwise equivalent to the commercial version.