Engineering analysis error estimation when removing finite-sized features in nonlinear elliptic problems

The paper provides novel approaches for a posteriori estimation of goal-oriented engineering analysis error caused by removing finite-sized negative features from a complex model, in the case of analysis of nonlinear elliptic physical phenomena. The features may lie within the model’s interior or along its boundary, and may be constrained with either Neumann or Dirichlet boundary conditions. The main use is for deciding whether detail design features can be removed from a model, to simplify meshing and engineering analysis, without unduly affecting analysis results. Error estimates are found using adjoint theory. Using a rigorous mathematical derivation, the error is first reformulated as a local quantity defined over the boundary of the feature to be suppressed, via linearization and Green’s theorem. This intermediate result still involves unknown terms, which we overcome in three ways. In one, an approximate upper bound of the error is obtained rigorously utilizing classical theories of differential operators; the others are heuristic practical approaches. The performance and the effectivity of these three different approaches are examined on 2D and 3D internal and boundary features, with Neumann and Dirichlet boundary conditions