Concept

Elliptic boundary value problem

Related publications (28)

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

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

ELSEVIER SCIENCE SA2022

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

Numerical homogenization methods for parabolic monotone problems

Assyr Abdulle

In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. ...

2016

An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient

Fabio Nobile, Lorenzo Tamellini, Francesco Tesei

In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version capable of using non-nested collocation points, and supporting quadrature and in ...

Springer2016

On a Lagrangian Formulation of the Incompressible Euler Equation

Hasan Inci

In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...

Global Science Press2016

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Daniel Kressner, André Uschmajew

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...

Elsevier Science Inc2016

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” ...

2016

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to ...

Elsevier2016

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