Questions tagged [variational-calculus]

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Solving a nonlinear poisson equation via variational minimization

I am kind of new in finite elements and I am solving simple "Poisson nonlinear" problem. $- \nabla ((1 + u^2) \nabla u) = f$ $u = 0 \ \text{on} \ \Omega $ I am using Newton solver, where I have ...
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Reference Request: Variational Problem

I want to solve approximately the following variational problem: Given a function $c:[-1,1]^2\rightarrow [0,1]$, constants $p_1...p_n\in \mathbb{R}^+$, $\alpha_1...\alpha_n\in \mathbb{R}$, and $\...
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functional second derivative

I'm trying to build a numerical solution for a parameter estimation problem of reaction-diffusion equation, using the adjoint method. To summarize it, I'm trying to minimize the function $$ G=\frac{...
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General-purpose Numerical Calculus of Variations Problem

Calculus of variations problems are generally cast in in the following simple form: find $u(t)$ that satisfies some boundary conditions and minimises $$ F[u] = \int_{t=0}^{t=t_f} f(u(t),u'(t),t) dt. $...