Finding finite element soluton for a PDE

In summary, a PDE is a mathematical equation used to model physical phenomena and involves multiple variables and partial derivatives. The finite element method is a numerical technique used to solve PDEs by discretizing them into smaller elements and solving them individually. To find a finite element solution for a PDE, the PDE must first be discretized, appropriate basis functions must be defined, and a system of linear equations must be constructed and solved using numerical methods. The advantages of using the finite element method for PDEs include its ability to handle complex geometries and provide accurate solutions, as well as its adaptivity and refinement capabilities. However, it may be computationally expensive and not suitable for certain types of PDEs.
  • #1
get2kool
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Find the Finite element solution for a equation:
(∂^2 u)/〖∂x〗^(2 ) +(∂^2 u)/〖∂y〗^2 +λu-c=0
using linear triangular finite elememts.
In the above equation u is scalar,λ is a constant and is a body force term(constant).

The boundary conditons are in terms of prescribed values of the function u or zero flux.
 
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  • #2
Have you made any attempt yourself? What exactly is meant by "linear triangular finite elements"?
 

Related to Finding finite element soluton for a PDE

1. What is a PDE?

A PDE, or partial differential equation, is a mathematical equation that involves multiple variables and their partial derivatives. It is commonly used to model physical phenomena such as heat transfer, fluid dynamics, and quantum mechanics.

2. What is the finite element method?

The finite element method is a numerical technique used to solve PDEs. It involves discretizing the PDE into smaller, simpler elements and solving them individually to approximate the solution of the entire PDE.

3. How do you find a finite element solution for a PDE?

To find a finite element solution for a PDE, you first need to discretize the PDE into smaller elements using a mesh. Then, you need to define the appropriate basis functions for each element and use them to construct a system of linear equations. Finally, you can solve this system of equations using numerical methods to obtain the finite element solution.

4. What are the advantages of using the finite element method for PDEs?

The finite element method offers several advantages for solving PDEs. It can handle complex geometries and irregular boundaries, it provides accurate solutions, and it allows for adaptivity and refinement of the mesh to improve the accuracy of the solution.

5. Are there any limitations to using the finite element method for PDEs?

While the finite element method has many advantages, it also has some limitations. It can be computationally expensive for problems with a large number of elements, and it may not be suitable for certain types of PDEs, such as those with discontinuous solutions or singularities.

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