Finite Element vs. Finite Volume

Thread starter Niles
Start date Feb 16, 2011
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Element Finite finite element Volume

In summary, Finite Element and Finite Volume methods are two numerical techniques used to solve partial differential equations (PDEs). While Finite Element method divides the problem domain into smaller elements and approximates the solution within each element, Finite Volume method divides the domain into control volumes and approximates the solution at the centroid of each volume. The accuracy of both methods depends on the type of problem being solved, with Finite Element method being better for irregular boundaries and Finite Volume method being better for discontinuous or varying coefficients. However, both methods are not applicable to all types of problems and are primarily used for solving PDEs in engineering and science applications. Some popular software packages for implementing these methods include ANSYS, COMSOL, and OpenFOAM.

Feb 16, 2011

Niles

Homework Statement

Hi guys

Is there a difference between finite element methods and finite volume methods? Or do they both rely on each other?

Niles.

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Feb 18, 2011

HenzNett

for finite element methods, the geometry is cut into meshes and you do piecewise approximation on each mesh.
for finite volume methods, approximations are done on the volume around node.

1. What is the main difference between Finite Element and Finite Volume methods?

Finite Element method is a numerical technique used to solve partial differential equations (PDEs) by dividing the problem domain into smaller elements and approximating the solution within each element using a finite number of basis functions. Finite Volume method, on the other hand, is a numerical method that divides the problem domain into control volumes and approximates the solution at the centroid of each control volume.

2. Which method is more accurate, Finite Element or Finite Volume?

Both Finite Element and Finite Volume methods have their own advantages and limitations, and their accuracy depends on the type of problem being solved. In general, Finite Element method is better suited for problems with irregular boundaries or complex geometry, while Finite Volume method is better for problems with discontinuous or varying coefficients.

3. Are Finite Element and Finite Volume methods applicable to all types of problems?

No, Finite Element and Finite Volume methods are primarily used for solving PDEs, particularly in engineering and science applications. They are not suitable for solving problems that can be solved analytically or with simpler numerical methods, such as ordinary differential equations.

4. What are some software packages used for implementing Finite Element and Finite Volume methods?

There are several software packages available for implementing Finite Element and Finite Volume methods, such as ANSYS, COMSOL, and OpenFOAM. These packages offer various features and capabilities for solving different types of problems, and are widely used in industry and research.

5. Which method is more computationally efficient, Finite Element or Finite Volume?

Again, the efficiency of Finite Element and Finite Volume methods depends on the problem being solved. In general, Finite Element method requires more computational resources due to the complexity of the basis functions, while Finite Volume method requires less due to its simpler approximation scheme. However, with advancements in computing technology, the difference in efficiency between the two methods is becoming less significant.