Solving Variational Equations with FreeFem++

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SUMMARY

This discussion centers on using FreeFem++ to solve variational equations within the finite element method framework. The specific variational equation referenced involves the integral of the product of partial derivatives of functions u and v over a domain T_h, equating it to the integral of a function f multiplied by v. The user seeks additional resources or literature to better understand this form of the variational equation, indicating a need for context and clarity regarding its application.

PREREQUISITES
  • Understanding of variational calculus
  • Familiarity with finite element methods
  • Basic knowledge of FreeFem++ syntax and functionality
  • Concept of weak formulations in differential equations
NEXT STEPS
  • Research "FreeFem++ documentation for variational equations"
  • Study "Finite Element Method: Linear Static Analysis" by Thomas J.R. Hughes
  • Explore "Variational Methods for the Numerical Solution of Partial Differential Equations" by G. A. S. de Oliveira
  • Learn about "Weak Formulation of PDEs" in the context of finite element analysis
USEFUL FOR

This discussion is beneficial for computational mathematicians, engineers utilizing finite element analysis, and researchers seeking to deepen their understanding of variational equations in FreeFem++.

urric
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Hi, sorry if this isn't the correct forum.
I'm trying freefem++ to solve some some problems with finite elements method, but in the documentation the following form of the variational equation is used:

[itex]\displaystyle\int_{T_{h}} (\frac{{\partial u}}{{\partial x}}\frac{{\partial v}}{{\partial x}} + \frac{{\partial u}}{{\partial y}}\frac{{\partial v}}{{\partial y}} )dxdy =\displaystyle\int_{T_{h}} fvdxdy[/itex]

I've searched for that form, but I wasn't able to find it

Could you tell me about a book or any source where I can study that form of the variational equation?

Thanks
 
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Looks strange without any imaginary units, time parameters or simply the order in the integral on the LHS.
Some context would be more than helpful.
 

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