Convergence analysis of an adaptive continuous interior penalty finite element method for the Helmholtz equation

Abstract

We are concerned with an adaptive continuous interior penalty finite element method for the Helmholtz equation. A convergence result with explicit constraints on the wave number k and the initial mesh size h0 is derived. In particular, it is shown that if k1+sh0s is sufficiently small, where 12<s≤1 depends on the regularity of the weak solution of the model problem, then the adaptive continuous interior penalty finite element method is a contraction with respect to the sum of the energy error and a scaled error estimator. Numerical experiments are provided to verify the theoretical findings and show advantages of the adaptive continuous interior penalty finite element method.