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Dynamic FEM: Can the timestep size be made extremely/arbitrarily small?

Jayadeep U. B.'s picture

Dear all,

I am in the process of developing an FE code, and doing the analysis, for a class of highly nonlinear, dynamic problems in elasticity using Total Lagrangian formulation.  It is well-known that for the accuracy purposes, we need to use a small timestep size (stability is not an issue for me as I am using an unconditionally stable implicit scheme for timestepping).

My doubt is whether I can use arbitrarily/extremely small time steps in the analysis for a given mesh?

One problem I can think of is the growth of numerical errors with the increase in number of steps (though it might remain within bounds, due to the stability of the scheme).  Are there any other issues associated with extremely small time steps?




Hi Jayadeep,

Even if you are using a implicit time scheme, the stability can not be assured if you are solving a highly nonlinear problem. So, the time step have to be reduced to get a converged and accurate solution.

About the smallness of time step, other than the computational cost it should not create any problem. But if you can afford a very small time step in implicit schemes, it will advisable to go for some explicit schemes which are conserving(Like explicit -Newmark's predictor corrector or variational integrators) in nature. This can improve the efficiency in computation without losing accuracy.




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