Equivalent of Automated Adaptive Mesh Refinefent in FEniCSx

Hi Everyone,

I am new to FEniCSx. I am converting one of my code from FEniCS to FEniCSx. I want to know if there are any equivalents of AdaptiveLinearVariationalSolver and AdaptiveNonlinearVariationalSolver in FEniCSx. I am not able to find these in the reference.

As far as I’m aware this was originally implemented in old DOLFIN in support of this paper around 10 years ago: https://arxiv.org/pdf/1204.6643.pdf.

The automated adaptivity implementation was never really maintained or developed further. It didn’t work in parallel and wasn’t modular to allow for custom adaptivity controls or error estimation.

Part of the philosophy of DOLFINx is to provide core features from which esoteric custom implementations can be developed. Automated adaptivity is one of these situations where research and implementation is user dependent and straightforward to build on top of DOLFINx.

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As a side note: automated goal-oriented adaptivity based on a posteriori estimates of the functionals’ errors via the DWR method is very straightforward, I have an implementation here. See, e.g., DWR Poisson, DWR Burgers and DWR compressible Navier-Stokes around a NACA0012.

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