Numerical approximation of elliptic interface problems via isoparametric finite element methods
This paper is concerned with the numerical approximation of elliptic interface problems via isoparametric finite element methods. First, a convergence analysis is carried which asserts that optimal rates of convergence are recovered in both the energy and the L2 L 2 norms. Subsequently, the efficiency of isoparametric finite elements for the problem at hand is also assessed via numerical experiments. Results both with smooth and piecewise regular interfaces are presented and discussed. The numerical predictions corroborate the theoretical results and they also indicate that second-order convergence is achieved in the L? L ? -norm. Comparisons between isoparametric finite elements, Lagrangian finite elements and the Immersed Interface Method are also performed.
interface problems isoparametric finite elements lagrangian finite elements broken sobolev spaces