The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
The finite element solution of parabolic equations
In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in -dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in -norm of the method.
The finite element solution of second order elliptic problems with the Newton boundary condition
The convergence of the finite element solution for the second order elliptic problem in the -dimensional bounded domain with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the and norms are obtained.
The finite volume method for an elliptic-parabolic equation.
The Fourier Analysis of Bezier Curves
The Fourier spectral method for the Sivashinsky equation.
The fourth order accuracy decomposition scheme for an evolution problem
In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.
The fourth order accuracy decomposition scheme for an evolution problem
In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.
The fractional transport equation: an analytical solution and a spectral approximation by Chebyshev polynomials.
The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method.
The Frequency Decomposition Multi-Grid Method. Part I: Application to Anisotropic Equations.
The fundamentality of sets of ridge functions.
The G method for heterogeneous anisotropic diffusion on general meshes
In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity,...
The Gauss center research in multiscale scientific computation.
The general form of local bilinear functions
The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces and is given.
The General Neville-Aitken-Algorithm and Some Applications.
The General Recurrence Relation for Divided Differences and the General Newton-Interpolation-Algorithm With Applications to Trigonometric Interpolation.
The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer.
The generalized finite volume SUSHI scheme for the discretization of the peaceman model
We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later,...
The geometric theory of Volterra integral equations - a preliminary report