Analysis of Finite Element Methods for the Nonlinear Dynamic Analysis of Shells.
Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D
So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
Analysis of mixed finite element methods on locally refined grids.
Analysis of mixed methods using conforming and nonconforming finite element methods
Analysis of multilevel decomposition iterative methods for mixed finite element methods
Analysis of parabolic difference schemes by Gerschgorin's method
Analysis of patch substructuring methods
Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one...
Analysis of Some Low-Order Finite Element Schemes for Mindlin-Reissner and Kirchhoff Plates.
Analysis of the potential formulation for the eddy current problem in a bounded domain.
Analysis of the Combined Finite Element and Fourier Interpolation.
Analysis of the Du Fort-Frankel method for linear systems
Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition
The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin methods. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown that due to...
Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains.
Analysis of the Kleiser-Schumann Method.
Analysis of the Schwarz algorithm for mixed finite elements methods
Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework.
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a set of assumptions...
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a...
Analysis tools for finite volume schemes
Anisotropic -adaptive method based on interpolation error estimates in the -seminorm
We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken -seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of the proposed...