Abstract:We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs, to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium solutions of nonlinear parabolic PDEs. The parameterization method provides an infinitesimal invariance equation for the invariant manifold, which we solve via a power series ansatz. A power matching argument leads to a recursive systems of linear elliptic PDEs -the so called … Show more
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