Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 16

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

A parameter-free smoothness indicator for high-resolution finite element schemes

100%
Kuzmin D., Schieweck F.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1478-1488
EN
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite elements. The discrete maximum principle is enforced using a linearized flux-corrected transport algorithm. The deactivation of the flux limiter in regions of high regularity makes it possible to avoid the peak clipping effect at smooth extrema without generating spurious undershoots or overshoots elsewhere.
2
Content available remote

A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations

100%
Renka R.
Open Mathematics
|
2013
|
tom 11
|
nr 4
630-641
EN
The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.
3
Content available remote

Discrete maximum principle for interior penalty discontinuous Galerkin methods

81%
Horváth T., Mincsovics M.
Open Mathematics
|
2013
|
tom 11
|
nr 4
664-679
EN
A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of these conditions. The theoretical results are illustrated with numerical examples.
4
Content available remote

Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems

81%
Axelsson O., Karátson J.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1441-1457
EN
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
5
Content available remote

Operator preconditioning with efficient applications for nonlinear elliptic problems

81%
Karátson J.
Open Mathematics
|
2012
|
tom 10
|
nr 1
231-249
EN
This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.
6
Content available remote

A parameter-free stabilized finite element method for scalar advection-diffusion problems

81%
Bochev P., Peterson K.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1458-1477
EN
We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use H(curl)-conforming edge elements to expand the resulting edge fluxes into an exponentially fitted flux field inside each element. Substitution of the nodal flux by this new flux completes the formulation of the method. Utilization of edge elements to define the numerical flux and the lack of stabilization parameters differentiate our approach from other stabilized methods. Numerical studies with representative advection-diffusion test problems confirm the excellent stability and robustness of the new method. In particular, the results show minimal overshoots and undershoots for both internal and boundary layers on uniform and non-uniform grids.
7
Content available remote

The discrete maximum principle for Galerkin solutions of elliptic problems

81%
Vejchodský T.
Open Mathematics
|
2012
|
tom 10
|
nr 1
25-43
EN
This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys the state of the art in the field of the discrete maximum principle and provides new generalizations of several results.
8
Content available remote

Functional a posteriori error estimates for incremental models in elasto-plasticity

81%
Repin S., Valdman J.
Open Mathematics
|
2009
|
tom 7
|
nr 3
506-519
EN
We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants and are valid for any conforming approximations regardless of the method used for their derivation. It is shown that the structure of error majorant reflects properties of the exact solution so that the majorant vanishes only if an approximate solution coincides with the exact one. Moreover, it possesses necessary continuity properties, so that any sequence of approximations converging to the exact solution in the energy space generates a sequence of positive numbers (explicitly computable by the majorant functional) that tends to zero.
9
Content available remote

Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients

81%
Guan X., Li M., He W., Jiang Z.
Open Mathematics
|
2014
|
tom 12
|
nr 11
1733-1747
EN
In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients.
10
Content available remote

Implicit a posteriori error estimation using patch recovery techniques

62%
Horváth T., Izsák F.
Open Mathematics
|
2012
|
tom 10
|
nr 1
55-72
EN
We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.
11
Content available remote

A comparison of some efficient numerical methods for a nonlinear elliptic problem

62%
Kovács B.
Open Mathematics
|
2012
|
tom 10
|
nr 1
217-230
EN
The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between them and analyzed their behavior, efficiency and mesh independence. We also compare the theoretical results to the numerical ones, and finally we propose some improvements which we also investigate.
12
Content available remote

Generalizations of the Finite Element Method

62%
Schweitzer M.
Open Mathematics
|
2012
|
tom 10
|
nr 1
3-24
EN
This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To this end, we consider meshbased and meshfree generalizations of the finite element method and the use of smooth, discontinuous, singular and numerical enrichment functions.
13
Content available remote

Spatially-dependent and nonlinear fluid transport: coupling framework

52%
Geiser J.
Open Mathematics
|
2012
|
tom 10
|
nr 1
116-136
EN
We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation methods or nonlinear solver methods. The nonlinear methods are based on characteristic methods and can be generalized numerically to higher-order TVD methods [Harten A., High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 1983, 49(3), 357–393]. In this article we will focus on the derivation of some analytical solutions for spatially dependent and nonlinear problems which can be embedded into finite volume methods. The main contribution is to embed one-dimensional analytical solutions into multi-dimensional finite volume methods with the construction idea of mass transport [Geiser J., Mobile and immobile fluid transport: coupling framework, Internat. J. Numer. Methods Fluids, 2010, 65(8), 877–922]. At the end of the article we present some results of numerical experiments for different benchmark problems.
14
Content available remote

Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

52%
Dimova M., Dimova S., Vasileva D.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1375-1391
EN
The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems - multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.
15
Content available remote

A Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region and its Applications

52%
Jiang Y., Ying J., Xie D.
Molecular Based Mathematical Biology
|
2014
|
tom 2
|
nr 1
EN
The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical solution. It is then used to verify a PBE finite element solver and applied to a numerical comparison study between a finite element solver and a finite difference solver. Such a study demonstrates the importance of retaining the interface conditions in the development of PBE solvers.
16
Content available remote

Anisotropic interpolation error estimates via orthogonal expansions

52%
Li M., Mao S.
Open Mathematics
|
2013
|
tom 11
|
nr 4
621-629
EN
We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.