Electrical engineering

Physics

Finite element method

Mixed finite element method

Mathematics

Engineering

Piecewise

Mathematical analysis

Gauss

Quantum mechanics

Quadrature (astronomy)

Superconvergence

Thermodynamics

Journal of Scientific Computing

We prove that the superconvergence of $$C^0$$ C0-$$Q^k$$ Qk finite element method at the Gauss–Lobatto quadrature points still holds if variable coefficients in an elliptic problem are replaced by their piecewise $$Q^k$$ Qk Lagrange interpolants at the Gauss–Lobatto points in each rectangular cell. In particular, a fourth order finite difference type scheme can be constructed using $$C^0$$ C0-$$Q^2$$ Q2 finite element method with $$Q^2$$ Q2 approximated coefficients.

Superconvergence of $$C^0$$-$$Q^k$$ Finite Element Method for Elliptic Equations with Approximated Coefficients