can finite element method be used to solve all space time problems with multiple dimensions?

Question

can finite element method be used to solve problems with multiple dimensions if we know the properties of each element such as the strain and stress relationships of each element to each other and the fluid and electromegatic flows in and out each elements by what comes in must go out principle? i can see that FEM would have applications from architecture, virtual reality (computer art) to structural, mechanical and electrical engineering and even medical imaging applications (things which we can see and can't see)?

Answer 1

Let's assume that we're addressing nD-T spacetimes, where n is an integer, and such that all local nD-T spacetimes can be approximated by (n+1)D linear manifolds. Furthermore, let's assume that we have physical laws for such nD-T spacetimes that are expressionable in the same Newtonian manner as those for 3D-T spacetimes. Then, yes, FEA schemes can be devised for computer simulations of such nD-T spacetimes. There is nothing mathematically special about 3D-T spacetimes that permits FEA methods to work and not in other nD-T spacetimes. Computer programming can handle n-dimensional data arrays just as handily as it can 3-dimensional data arrays. Problems arises when physical simulation is not possible by approximation with (n+1) linear manifolds, such as quantum field theories or non-locality. Then such simulation of quantum reality might only be possible with quantum FEA computation, not conventional.

It should be added that a lot of laws of physics actually have no mathematical counterpart in higher dimensions, which makes the question of number of dimensions for physical reality a fascinating one. In other words, a lot of things we take for granted in 3D-T spacetimes is impossible in higher dimensions. That strongly suggests some of the reasons why we exist in 3D-T spacetime.

Answer 2

x=2 y=4

Answer 3

What scythian said.