Differebce between finite volume element difference
Answers
Answer:
Explanation:
iscretizes the domain into finite elements and calculates the properties in every node.
Shape functions or basis functions are used to interpolate inside the finite element, the solutions obtained at these nodes. Generally linear interpolation is acceptable. If this is not the case, quadratic or cubic shape functions can also be used at the expense of computational time. It is always a custom during our FE lecture sessions at the university that, when this topic is taught, a simple problem (Ex: Cantilever beam) is asked to solve using both linear and quadratic shape functions to understand the difference.
Every finite element is formulated with a stiffness matrix, which is called local stiffness matrix. These local stiffness matrices are assembled which results in global stiffness matrix of the whole structure under investigation
As a result, the partial differential equations are converted into a set of algebraic equations which are comparatively easier to solve.
There are already established subroutines to solve these algebraic equations
FEM is the most commonly used and it is efficient for all geometries including ones with complicated shapes and features
Finite Volume Method – FVM
The properties are calculated for every cell instead of a node
Based on the integral form of conservation laws and can handle discontinuities in solutions. In simple terms, what comes in, must go out.
FVM approximates the value of the integral on the reference cell
Efficient in solving fluid flow problems
Like FEM, lot of established and theoretically proven subroutines are in place for FVM which can be directly implemented in your code.
I have written just a very basic and introductory piece on the three numerical methods in solving a partial differential equation. For further understanding, these books could be referred.