A-Posteriori Error Estimates for non-linear FEM Problems based on Matrix Reuse
Lutz Grosz
Abstract:
A new a-posteriori error estimate for the finite element solution of
non-linear variational problem is developed. The error estimate is
calculated by the solution of an error equation with the same
stiffness matrix as used for the calculation of the finite element
solution. This allows to profit from costly operations of the finite
element analysis. It is shown that the a-posteriori error estimate is
equivalent to the true error. By balancing the estimated discretisation
error and termination error an optimal stopping criterion for iterative
solvers used to solve the discrete problem is established. Examples show
the flexibility and robustness of the error estimate.
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