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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra

We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure systems. The methods are based on a new family of mixed finite elements, which are enhanced Raviart–Thomas spaces with bubbles that are curls of specially chosen polynomials. The velocity degrees of freedom of the new spaces can be associated with the points of tensor-product Gauss–Lobatto quadrature rules, which allows for local velocity elimination and leads to a symmetric and positive definite cell-based system for the pressures. We prove optimal [Formula: see text]th order convergence for the velocity and pressure in their natural norms, as well as [Formula: see text]st order superconvergence for the pressure at the Gauss points. Moreover, local postprocessing gives a pressure that is superconvergent of order [Formula: see text] in the full [Formula: see text]-norm. Numerical results illustrating the validity of our theoretical results are included.

Mathematics↗
DOE OSTI2018

Smoothness of Generalized Solutions of the Dirichlet Problem for Strongly Elliptic Functional Differential Equations with Orthotropic Contractions

In the disk, we consider the first boundary-value problem for a functional differential equation containing transformations of orthotropic contractions of independent variables of the unknown function. We study the smoothness of generalized solutions inside special-type subdomains and near their boundaries and pose strong ellipticity conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On the Dirichlet problem for a nonlinear elliptic equation

We prove the existence of an infinite set of solutions to the Dirichlet problem for a nonlinear elliptic equation of the second order. Such a problem for a nonlinear elliptic equation with Laplace operator was studied earlier by Krasnosel'skii, Bahri, Berestycki, Lions, Rabinowitz, Struwe and others. We study the spectrum of this problem and prove the weak convergence to 0 of the sequence of normed eigenfunctions. Moreover, we obtain some estimates for the 'Fourier coefficients' of functions in W{sub p,0}{sup 1}(Ω). This allows us to improve the preceding results. Bibliography: 8 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Model Elliptic Boundary-Value Problems for Pseudodifferential Operators in Canonical Nonsmooth Domains

We consider a simplest elliptic pseudodifferential equation in a multi-dimensional cone (multi-dimensional angle) and describe all possible structures of its solutions related to the wave factorization of the elliptic symbol. Depending on the index of wave factorization, we consider various statements of well-posed boundary-value problems. The existence of solutions is studied in Sobolev–Slobodetskii spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Approximate solutions to a nonintegrable problem of propagation of elliptically polarised waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes

Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

On Some Degenerate Elliptic Equations Arising in Geometric Problems

We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably defined generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller–Osserman on the zero-order term is necessary and sufficient for the existence of entire weak subsolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Classical Solvability of the Radial Viscous Fingering Problem in a Hele–Shaw Cell with Surface Tension

We consider the one-phase problem on radial viscous fingering structures in a Hele–Shaw cell with surface tension. This problem is a nonlinear free-boundary problem for elliptic equations. Unlike the Stefan problem for the heat equation, we deal with a problem of hydrodynamic type. We establish the classical solvability of the one-phase Hele–Shaw problem with radial geometry by using the same method as that used for the Stefan problem and justifying the vanishing coefficient of the time-derivative in the parabolic equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain

An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted Hölder spaces. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The nonconforming virtual element method for eigenvalue problems

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2 -inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

The nonconforming Virtual Element Method for eigenvalue problems

In this work, we analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case. We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the $L^2$-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problem. The proposed schemes provide a correct approximation of the spectrum, in particular we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A Control Variate Method for Probabilistic Performance Assessment. Improved Estimates for Mean Performance Quantities of Interest

We present a method of control variates for calculating improved estimates for mean performance quantities of interest, E(PQI) , computed from Monte Carlo probabilistic simulations. An example of a PQI is the concentration of a contaminant at a particular location in a problem domain computed from simulations of transport in porous media. To simplify the presentation, the method is described in the setting of a one- dimensional elliptical model problem involving a single uncertain parameter represented by a probability distribution. The approach can be easily implemented for more complex problems involving multiple uncertain parameters and in particular for application to probabilistic performance assessment of deep geologic nuclear waste repository systems. Numerical results indicate the method can produce estimates of E(PQI)having superior accuracy on coarser meshes and reduce the required number of simulations needed to achieve an acceptable estimate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Solution of Boundary Value Problems in Cylinders with Two-Layer Film Inclusions

We consider the class of boundary value problems for elliptic, parabolic, and hyperbolic equations in cylinders separated by a two-layer film into two half-cylinders. We prove the existence and uniqueness theorem and express the solutions in terms of solutions to analogous classical problems in cylinders without films.

97 MATHEMATICS AND COMPUTING↗