# Element Definition and 10 Discussions

The finite element method (FEM) is a widely used method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.
The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

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1. ### I Is there an algebraic derivation of the area element in polar coordinates?

There is a simple geometric derivation of the area element ## r dr d\theta## in polar coordinates such as in the following link: http://citadel.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node4.html Is there an algebraic derivation as well beginning with Cartesian coordinates and using ##...
2. ### Oddly specific number of elements

There are 118 elements known to man, and some scientists like Feynman think that element 137 might be the end of the Periodic Table. Isn't that oddly specific? To me, it feels like it is completely random and of no significance. What is going on here? Is there a constant that relates to this...
3. ### How to control the weight of an object?

Hello everyone, First off, i would like to apologize for any spelling errors. I am Portuguese and my english is going to be very simple. I am in the process of building something and i am reaching out to the physics community for help solving a problem. I am a CNC programmer and while i was in...
4. ### Which elements form covalent bonds?

This might be a very basic question. What are the elements that are in the world of creating covalent bonds, distinguishing themsevels from the elements that never form covalent bonds? Many thanks!
5. M

### A What is the value of optical effective electron mass for tin

What is the value of optical effective electron mass for tin metal (white tin)? What is the value of mean free path for electron of tin metal? At least give me some websites or papers where I can find it?
6. ### B Why only certain colors in emission spectrum are visible?

Why are only certain colors of the emission spectrum in Hydrogen visible?
7. ### Electric Element Voltage Specifications?

Hello, I have a question about electric elements and their corresponding voltages. I am looking at powering a 1500W 120VAC element out of an ordinary kettle with a DC voltage supplied by solar panels. So, from what I understand, 120VAC represents the RMS voltage meaning that it would require...