Zoe:
These sorts of issues often take a bit of time to debug. But here are a few
questions:
I would greatly appreciate any insights or suggestions you might have
regarding this issue. Here are a few things I suspect could be contributing to
the problem:
1. *Time Integration Scheme*: I may not be implementing the second-order
time-stepping correctly, especially in handling the nonlinear terms.
In that case, what happens if you choose a solution that is time-independent?
Do you obtain the expected convergence rate?
2. *Finite Element Discretization*: I’m currently using standard linear
elements, but I wonder if higher-order elements are needed for this scheme
to achieve second-order accuracy.
What happens if you choose a higher-order element?
3. *Energy Stability*: There could be issues with maintaining energy
stability in the scheme, which might be affecting the overall accuracy.
Have you tried computing the energy in the (numerical) solution to test
whether that is an issue?
Best
Wolfgang
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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