The increasing use of MR elastography demands that fast, robust, and out-of-the-box reconstruction methods are available. A new local direct method is presented here to fit these needs. The method utilizes the finite element method, assumes that stiffness is locally homogeneous, and includes additional advancements that improve quality and robustness. Efficacy of the proposed method is demonstrated across phantoms and volunteer data in the brain and breast. The method is contrasted with other standard techniques, showing similar or improved accuracy and robustness, improved computational cost and an independence from regularization parameters.