On block diagonal and Schur complement preconditioning.
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On Composite Mesh Difference Methods for Hyperbolic Differential Equations.
On computing the pressure by the p version of the finite element method for Stokes problem.
On Conforming Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations.
On Conjugate Gradient Type Methods and Polynomial Preconditioners for a Class of Complex Non-Hermitian Matrices.
On Constrained Multivariate Splines and Their Approximations.
On convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations.
On discontinuous Galerkin method and semiregular family of triangulations
Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.
On equilibrium finite elements in three-dimensional case
The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.
On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations.
On estimation of diffusion coefficient based on spatio-temporal FRAP images: An inverse ill-posed problem
We present the method for determination of phycobilisomes diffusivity (diffusion coefficient ) on thylakoid membrane from fluorescence recovery after photobleaching (FRAP) experiments. This was usually done by analytical models consisting mainly of a simple curve fitting procedure. However, analytical models need some unrealistic conditions to be supposed. Our method, based on finite difference approximation of the process governed by the Fickian diffusion equation and on the minimization of an...
On exact results in the finite element method
We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution . We show that the Galerkin approximation of based on the so-called biharmonic finite elements is independent of the values of in the interior of any subelement.
On existence of the weak solution for nonlinear diffusion equation
The paper concerns the existence of bounded weak solutions of a anonlinear diffusion equation with nonhomogeneous mixed boundary conditions.
On FE-grid relocation in solving unilateral boundary value problems by FEM
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the...
On finite difference schemes of high order accuracy for elliptic equations with mixed derivatives
On finite element approximation of fluid structure interaction by Taylor-Hood and Scott-Vogelius elements
This paper focuses on mathematical modeling and finite element simulation of fluid-structure interaction problems. A simplified problem of two-dimensional incompressible fluid flow interacting with a rigid structure, whose motion is described with one degree of freedom, is considered. The problem is mathematically described and numerically approximated using the finite element method. Two possibilities, namely Taylor-Hood and Scott-Vogelius elements are presented and implemented. Finally, numerical...
On Finite Element Approximation of the Gradient for Solution of Poisson Equation.
On Finite Element Approximations to Time-Dependent Problems.
On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems
We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is...