Local error analysis for the Stokes equations with a punctual source term
The paper concerns local error analysis for the Stokes equations with a punctual source term. The authors establish in dimension 2 local error estimates for the Stokes problem with a punctual force in source term, and show a quasioptimal convergence in the \(H^1\times L^2\)-norm for a \(P_k/P_{k-1}\)-finite element method, \(k>=2\), and for the \(P_1b/P_1\). The proof is based on local Arnold and Liu error estimates, a weak version of the Aubin-Nitsche duality lemma applied to the Stokes problem and discrete inf-sup conditions. These theoretical results are generalized to a wide class of finite element methods.
scientific article; zbMATH DE number 6969647
scientific article