Finite element methods yield weak solutions to partial differential equations (PDEs), which are only valid in integral form. If a classical (strong) solution exists, it is also a weak solution; however, weak solutions may exhibit discontinuities and can differ significantly from classical solutions locally while remaining accurate globally. Numerical errors in finite element software, such as those caused by hourglassing and shear locking, can lead to discrepancies between weak and strong solutions. Accurate modeling is crucial to minimize errors stemming from discretization and boundary conditions.
PREREQUISITESEngineers, researchers, and students involved in finite element analysis, particularly those focusing on numerical methods and error minimization in structural simulations.
Sorry there was a typo in my original post, should change 'analytic' to 'strong'.S.G. Janssens said:By "analytic" do you mean "classical", as in: satisfying the differential form of the PDE?
A classical solution need not exist, and weak solutions may admit discontinuities. In that case, a weak solution would be very far from "differentiable", and the answer to your question would be "yes".
On the other hand, if a classical solution exists, then it is also a weak solution. If, moreover, weak solutions are unique, then the classical solution and the weak solution are the same, and course the answer to your question would be "no".
(This all assumes that the software accurately reproduces the weak solution, including its possible discontinuities.)
I use quadratic elements and U-P nearly impressible algorithm, will these still happen?caz said:There are things like hourglassing and shear locking.