Dear Community members! I started to learn FEniCS using the book by Langtangen and Logg. When solving the Poisson-equation, it is suggested, to reformulate the equation \Delta u = -f to the variational formulation, i.e. multiply by v \in H^1_0 and integrate by parts to get \int \nabla u \cdot…

Hello, Higher order Lagrange elements are still not C^2 continuous, as it is only enforced that their value is the same on mesh entities shared between two cells. In order to have C^2 continuity, you need to have DOFs that endure that the derivative is continuous between cells. For example, Hermit…

I’m guessing some (or maybe all) the coefficients of your solution are nan, which is why you get the error you’re seeing. Degree 1 Lagrange basis functions are continuous between cells, but do not have a continuous derivative. (ie u\in C^1, but u\not\in C^2 as you said). This means that \Delta u is…

Hi Mathew, thank you for your quick answer! So FEniCS does not provide C^2 basis functions - that implies, any equation has to be written in a formulation, where strictly u\in C^1. Does that mean for an equation like this \Delta(\Delta u) = -f one needs to apply integration by parts several time…

In addition to @mscroggs ’s points, you could consider weakly enforcing continuity of the first derivative of your FE solution as part of the C^2 requirement. There’s a very old demo which could easily be updated for dolfinx. There’s also @kamensky ’s tIGAr which offers C^k continuity with a spline b…

Solve PDEs without transforming to variational formulation

variational formulation

kamensky April 29, 2022, 2:11pm 6

I’ll also mention an old post here, where I answered a similar question in some more detail.

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Solve PDEs without transforming to variational formulation

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