Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces (Q2838589)

The article is concerned with linear diffusion equations \(\text{div}(A\text{\,grad\,}u)= f\) on a bounded domain in 2D or 3D, with a piecewise continuous matrix coefficient \(A\). The particular issue is that the interfaces between the domains of constancy of \(A\) are rough and ``complicated''.NEWLINENEWLINE The authors use a mixed modeling-discretization strategy for the numerical solution of such problems: The complicated interfaces are approximated by a sequence of simpler ones, and the simplified problems are discretized using a sequence of meshes. For both the modeling and the discretization error, a posteriori error estimates are proposed which can be used to equilibrate between the two errors. Several numerical tests are presented to illustrate the results.