The high-order Shifted Boundary Method and its analysis

The Shifted Boundary Method (SBM) is an approximate domain method for boundary value problems , in the broader class of unfitted/embedded/immersed methods, that has proven efficient handling partial differential equation with complex geometries . key feature SBM a shift location where conditions are applied – from true to surrogate and appropriate modification (again, ) conditions, order reduce consistency error. This paper presents high-order version method, its mathematical analysis, numerical experiments. proposed retains optimal accuracy any finite element interpolation spaces despite piecewise linear. As such, approach bypasses problematic issue meshing body-fitted representations, without need data structures integration on cut cells. • presented. unfitted FEM does not require defined domain, modified conditions. optimally accurate even if affine. Proofs stability, convergence, L 2 -error estimates included.