Basic error estimates for elliptic problems

The Lagrange-Galerkin method is a numerical technique for solving convection -- dominated diffusion problems, based on combining a special discretisation of the Lagrangian material derivative along particle trajectories with a Galerkin finite element method We present optimal error estimates for the Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes equations in a velocity/pressure formulation The method is shown to be nonlinearly stable

Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.

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NURBS-enhanced finite element method (NEFEM)

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NURBS-Enhanced Finite Element Method (NEFEM)

: In the paper a general approximation theory for the eigenvalues and corresponding subspaces of generalized eigenfunctions of a certain class of compact operators is developed. This theory is then used to obtain rate of convergence estimates for the errors which arise when the eigenvalues of non-selfadjoint elliptic partial differential operators are approximated by Rayleigh-Ritz-Galerkin type methods using finite dimensional spaces of trial functions, e.g. spline functions. The approximation methods include several in which the functions in the space of trial functions are not required to satisfy any boundary conditions. (Author)

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R. Mcleod

Papers

Curved elements in the finite element method

The Use of Parabolic Arcs in Matching Curved Boundaries in the Finite Element Method

The Construction of Basis Functions for Curved Elements in the Finite Element Method