We present an expanded mixed finite element method for solving second-order elliptic partial differential equations on geometrically general domains. For the lowest-order Raviart–Thomas approximating spaces, we use quadrature rules to reduce the method to cell-centered finite differences, possibly enhanced with some face-centered pressures. This substantially reduces the computational complexit...

In this paper we make a thorough study of the use of the finite element method to numerically compute harmonic maps from parametric surfaces to the plane. There are essentially two choices to be made in the FE method: (1) which elements and (2) which quadrature. We show that by using linear elements and point-based linear quadrature the method reduces to the cotangent method studied by Dziuk, P...

A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H2-norm error estimate is obtained for th...

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlineariti...

where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...