The effect of numerical integration in the FEM for elliptic problems with mixed boundary conditions (opens in new tab)

This paper investigates the impact of quadrature accuracy for volume and face integrals in the finite element method using $p$-th order polynomial shape functions for elliptic problems with mixed Dirichlet and Robin boundary conditions. The optimal $p$-th order $H^1$-convergence is maintained when numerical integration with algebraic precision at least $2p-2$ for volume terms and at least $2p-1$ for face terms is adopted. For $L^2$-error, we ach...