Interpolation of non-smooth functions on anisotropic finite element meshes
Interpolation of non-smooth functions on anisotropic finite element meshes
In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.
Interpolation Remainder Theory from Taylor Expansions on Triangles.
Inverted finite elements : a new method for solving elliptic problems in unbounded domains
In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.
Inverted finite elements: a new method for solving elliptic problems in unbounded domains
In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.
Isogeometric analysis for fluid flow problems
The article is devoted to the simulation of viscous incompressible fluid flow based on solving the Navier-Stokes equations. As a numerical model we chose isogeometrical approach. Primary goal of using isogemetric analysis is to be always geometrically exact, independently of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization techniques SUPG and PSPG. All methods mentioned in the paper are demonstrated...
Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients
Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field and displacement...
Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients
Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field and displacement...
Isotropic and anisotropic a posteriori error estimation of the mixed finite element method for second order operators in divergence form.
Iterative refinement of finite element approximations for elliptic problems
Iteratively solving a kind of Signorini transmission problem in a unbounded domain
In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...
Iteratively solving a kind of signorini transmission problem in a unbounded domain
In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...
-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes
An -estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space.
-convergence of finite element Galerkin approximations for parabolic problems
-convergence of saddle-point approximations for second order problems
-error estimate for a system of elliptic quasivariational inequalities.
-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities.
-error estimates for variational inequalities with Hölder continuous obstacle
L... Stability of Finite Element Approximations to Elliptic Gradient Equations.
L2 Error Estimates for Finite Elements with Interpolated Boundary Conditions.