1. A method for modeling a subsurface reservoir system, the method comprising:generating, with a computer, a background mesh that does not honor at least one subsurface feature included in the subsurface reservoir system;
splitting, with a computer, the background mesh along the subsurface feature included in the subsurface reservoir system such that a resulting mesh honors a geometry of the subsurface features;
identifying, with a computer, element faces or edges where the resulting mesh is non-conforming and/or the element faces or edges lie on subsurface features; and
performing a computer-based numerical simulation utilizing the resulting mesh to model at least one fluid-related or geomechanical reservoir response, wherein mass or traction balance is enforced on the identified element faces or edges.