A defect-correction method for unsteady conduction convection problems I: spatial discretization

Abstract

In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct this solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property.

Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

“…High efficient finite element schemes have been researched further in recent years; for example, see [22,[25][26][27][28][29][30][31]. Based on these works, this paper combines the shifted-inverse iteration and spectral method to propose an efficient scheme.…”

Convergence Analysis for the Iterated Defect Correction Scheme of Finite Element Methods on Rectangle Grids

“…The iterated defect-correction method is an improvement technique for increasing the accuracy of a numerical solution. For more applications of iterated defect-correction methods, we refer the interested readers to [5] for convection-diffusion equations, [1] for adaptive iterated defect-correction methods of convection-diffusion problems, [6] for adaptive iterated defectcorrection methods of viscous incompressible problems, [4] for steady-state viscoelastic problems, [9] for singularly perturbed convection-diffusion problems, [10] for singular initial value problems, [11,12,16] for the time-dependent Navier-Stokes equations, [13] for the stationary Navier-Stokes equation, [19] for eigenvalue problems from quantum chemistry, and [18] for unsteady conduction convection problems.…”

Modified characteristics mixed defect-correction finite element method for the time-dependent Navier–Stokes problems

“…In [39], Stetter exposed the common structural principle of all these techniques and exhibit the principal modes of its implementation in a discretization context. In [40][41][42], we give the defectcorrection finite element method for the conduction-convection problems.…”