Superconvergence of the split least-squares method for second-order hyperbolic equations



This article studies superconvergence phenomena of the split least-squares mixed finite element method for second-order hyperbolic equations. By selecting the least-squares functional properly, the procedure can be split into two independent symmetric positive definite subprocedures, one of which is for the primitive unknown and the other is for the flux. Based on interpolation operators and an auxiliary projection, superconvergent H1 error estimates for the primary variable u and L2 error estimates for the introduced flux variable σ are obtained under the standard quasiuniform assumptions on finite element partition. A numerical example is given to show the performance of the introduced scheme. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 222-238, 2014