1. A method of refining Arbitrary Lagrangian-Eulerian (ALE) elements of a finite element analysis (FEA) model used in a time-marching simulation that simulates physical phenomena of a physical domain, said method comprising: receiving a FEA model representing a physical domain with a plurality of ALE elements in a computer system having an ALE based FEA application module installed thereon, wherein each of the ALE elements is an eight-node solid finite element having six element faces; and obtaining simulated physical phenomena of the physical domain by conducting a time-marching simulation using the FEA model subject to a user specified condition, said conducting the time-marching simulation comprising: upon detecting a user defined triggering condition, refining certain ones of the ALE elements by dividing each of said certain ones of the ALE elements into a plurality of child elements, determining and creating a list of neighbor elements of said each of the ALE elements, and determining which element face of said each of the ALE elements is next to a neighbor element without refinement; in a first solution phase at each time step, obtaining simulated responses in form of deformed nodal positions of said each of the ALE elements by performing a FEA of the FEA model; and in a second solution phase at said each time step, mapping simulated responses to another FEA mesh which includes calculating at least one material flux at each element face of said each of the ALE elements based on said deformed nodal positions and nodal positions of said another FEA mesh, determining a donor and at least one corresponding receptor at said each element face, said at least one material flux flowing out said donor and into said at least one corresponding receptor, calculating respective portions of said at least one material flux to be received in said at least one corresponding receptor when said each element face is located between an unrefined element and a refined element, otherwise the respective portions are calculated in said donor, and distributing said respective portions from said donor to said at least one corresponding receptor.