Supplemental: Higher-Order Finite Elements for Embedded Simulation

Whereas measuring convergence rates for standard finite element discretizations is fairly straightforward, the measurement for embedded methods is more complicated by the need to design a measurement scheme which takes into account the precision with which the embedded domain is correctly captured. We discuss this problem more in detail in the following, and describe the setup we use to verify the convergence rate of the Finite Cell Method for a family of uniform background meshes with a non-trivial embedded geometry.