Structure et estimations de coefficients d'erreurs
Structure et estimations de coefficients d'erreurs
Superapproximation of the partial derivatives in the space of linear triangular and bilinear quadrilateral finite elements
A method for the second-order approximation of the values of partial derivatives of an arbitrary smooth function in the vertices of a conformal and nonobtuse regular triangulation consisting of triangles and convex quadrilaterals is described and its accuracy is illustrated numerically. The method assumes that the interpolant in the finite element space of the linear triangular and bilinear quadrilateral finite elements from is known only.
Superconvergence analysis and a posteriori error estimation of a Finite Element Method for an optimal control problem governed by integral equations
In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type a posteriori error estimator is provided, which can be used for adaptive mesh refinement.
Superconvergence analysis of approximate boundary-flux calculations.
Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations
We present a unified approach to studying the superconvergence property of the spectral volume (SV) method for high-order time-dependent partial differential equations using the local discontinuous Galerkin formulation. We choose the diffusion and third-order wave equations as our models to illustrate approach and the main idea. The SV scheme is designed with control volumes constructed using the Gauss points or Radau points in subintervals of the underlying meshes, which leads to two SV schemes...
Superconvergence by Steklov averaging in the finite element method
The Steklov postprocessing operator for the linear finite element method is studied. Superconvergence of order 𝓞(h²) is proved for a class of second order differential equations with zero Dirichlet boundary conditions for arbitrary space dimensions. Relations to other postprocessing and averaging schemes are discussed.
Superconvergence for a Mixed Finite Element Method for Elastic Wave Propagation in a Plane Domain.
Superconvergence for rectangular mixed finite elements.
Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method
This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.
Superconvergence of mixed finite element methods for parabolic equations
Superconvergence of mixed finite element semi-discretizations of two time-dependent problems
We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation...
Superconvergence of the gradient of finite element solutions
Superconvergence Phenomenon in the Finite Element Method Arising from Averaging Gradients.
Superconvergence results for linear triangular elements
Superlinear CG convergence for special right-hand sides.
Sur la convergence des méthodes d'éléments finis nonconformes pour des problèmes linéaires de coques minces.
Sur la convergence des schémas aux différences finies pour des équations elliptiques du quatrième ordre avec des solutions irrégulières. (Convergence of finite difference schemes for fourth order elliptic equations with irregular solutions).
Sur la convergence numérique de différentes méthodes de décomposition pour une classe de problèmes elliptiques.
Sur la méthode des éléments finis hybrides pour le problème biharmonique.