### Convergence of P3 elements for multimesh poisson problem

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Hi,

I am doing a project using multimesh formulations in FEniCS. The test case is having one square mesh overlapped by another, smaller, square mesh and solving poisson with Dirichlet BCs, and Nitsches method for connecting the two meshes and stabilization over the overlapped part of the cut elements (quite like multminesh-poisson DOLFIN demo but with only two, stationary, meshes). However, when examining the convergence (L2 and H1), I get the expected EOCs for P1 and P2 elements, but for P3 (or higher order) elements the errors are larger than for P1 or P2 elements, and we do not see the expected EOCs. Is there some setting which need to be changed, for instance quadrature order for cut elements?

I am doing a project using multimesh formulations in FEniCS. The test case is having one square mesh overlapped by another, smaller, square mesh and solving poisson with Dirichlet BCs, and Nitsches method for connecting the two meshes and stabilization over the overlapped part of the cut elements (quite like multminesh-poisson DOLFIN demo but with only two, stationary, meshes). However, when examining the convergence (L2 and H1), I get the expected EOCs for P1 and P2 elements, but for P3 (or higher order) elements the errors are larger than for P1 or P2 elements, and we do not see the expected EOCs. Is there some setting which need to be changed, for instance quadrature order for cut elements?

Community: FEniCS Project

What is the meaning of "quadratic mesh" ?

written
7 months ago by
Praveen C

I meant to say square mesh, will edit the post.

written
7 months ago by
Carl Holmberg

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