Stable finite element methods for the Stokes problem.
Statistical study of Navier-Stokes equations, I
Steady compressible Oseen flow with slip boundary conditions
We prove the existence of solution in the class H²(Ω) × H¹(Ω) to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class . The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary....
Stick-slip transition capturing by using an adaptive finite element method
The numerical modeling of the fully developed Poiseuille flow of a newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
Stick-slip transition capturing by using an adaptive finite element method
The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the...
Stream Vectors in Three Dimensional Aerodynamics.
Streamline diffusion finite element method for quasilinear elliptic problems.
Strong convergence estimates for pseudospectral methods
Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.
Strongly regular family of boundary-fitted tetrahedral meshes of bounded domains
We give a constructive proof that for any bounded domain of the class there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by Křížek and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated from below...
Stručná historie metody konečných objemů
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.