Finding finite element soluton for a PDE

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SUMMARY

The discussion focuses on finding the finite element solution for the partial differential equation (PDE) given by (∂²u/∂x²) + (∂²u/∂y²) + λu - c = 0, utilizing linear triangular finite elements. The equation involves a scalar function u, a constant λ, and a body force term c. Participants emphasize the importance of understanding boundary conditions, which can be either prescribed values of u or zero flux conditions. Clarification is sought regarding the definition and application of linear triangular finite elements in this context.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with finite element analysis (FEA)
  • Knowledge of boundary conditions in mathematical modeling
  • Basic concepts of linear triangular finite elements
NEXT STEPS
  • Research the implementation of finite element methods (FEM) for solving PDEs
  • Study the formulation and application of linear triangular finite elements
  • Explore boundary condition types and their implications in FEA
  • Learn about numerical solvers for PDEs, such as COMSOL Multiphysics or ANSYS
USEFUL FOR

Mathematicians, engineers, and researchers involved in computational mechanics, particularly those working with finite element methods for solving partial differential equations.

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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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Have you made any attempt yourself? What exactly is meant by "linear triangular finite elements"?
 

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