Publications related to Elliptic boundary value problem

Conservation of Forces and Total Work at the Interface Using the Internodes Method

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...

2022

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

Jan Sickmann Hesthaven, Lijing Zhao

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...

SCIENCE PRESS2020

On sums of eigenvalues of elliptic operators on manifolds

Joachim Stubbe

We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kroger's bound ...

European Mathematical Soc2017

Asymptotic bifurcation and second order elliptic equations on R-N

Charles Stuart

This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear ellipt ...

Elsevier Science Bv2015

Adaptive reduced basis finite element heterogeneous multiscale method

Assyr Abdulle, Yun Bai

An adaptive reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is proposed for elliptic problems with multiple scales. The multiscale method is based on the RB-FE-HMM introduced in [A. Abdulle, Y. Bai, Reduced basis finite element het ...

Elsevier2013

Edge stabilization for the generalized Stokes problem: A continuous interior penalty method

Erik Burman

In this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stability is obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can be seen as a higher o ...

2006

Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity

Gianluigi Rozza

We present an application in multi-parametrized sub-domains based on a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with affine parameter dependence (reduced-basis methods) ...

2005

Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence

Erik Burman

We analyze a nonlinear shock-capturing scheme for H1-conforming, piecewise-affine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasi-uniformity property and the Xu- ...

2005