Results 71 to 80 of about 12,245,009 (305)

Dirichlet problem Characterization of regularity

manuscripta mathematica, 1994
The author studies the regularity of the solutions to the Dirichlet problem \[ Lu\equiv -(a_{ij} u_{x_ i} )_{x_ j}= f \quad\text{in }\Omega, \qquad u=0 \quad \text{in }\partial\Omega \tag{1} \] where \(\mu\) is a given bounded variation measure on \(\Omega\) (bounded open subset of \(\mathbb{R}^ n\)), \(a_{ij}= a_{ji}\in L^ \infty (\Omega)\), \(i,j= 1,\
openaire   +2 more sources

Reflective Pathways: Integrating Empathy Into the STEM Student Experiences

Future in Educational Research, EarlyView.
ABSTRACT The growing demand for a globally competent STEM workforce showcases the importance of embedding empathy into undergraduate education. As a core dimension of global competence, empathy enables individuals to engage diverse perspectives and navigate collaborative challenges.
Aparajita Jaiswal, Nathan S. Bitner, Gaurav Nanda, Muna Sapkota   +3 more
wiley   +1 more source

Impact of Uncertain Parameters on Navier–Stokes Equations With Heat Transfer via Polynomial Chaos Expansion

International Journal for Numerical Methods in Fluids, EarlyView.
This study investigates the impact of uncertain parameters on Navier–Stokes equations coupled with heat transfer using the Intrusive Polynomial Chaos Method (IPCM). Sensitivity equations are formulated for key input parameters, such as viscosity and thermal diffusivity, and solved numerically using the Finite Element‐Volume method.
N. Nouaime, B. Després, M. A. Puscas, C. Fiorini   +3 more
wiley   +1 more source

The Dirichlet problem for nonlocal operators [PDF]

, 2013
In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the “boundary data” are prescribed on the complement of a given bounded ...
Matthieu Felsinger, M. Kassmann, P.-G. Voigt   +2 more
semanticscholar   +1 more source

Efficient Numerical Framework for Geothermal Energy Production Optimization in Fracture‐Controlled Reservoirs

International Journal for Numerical Methods in Fluids, EarlyView.
We introduce an efficient open‐source numerical framework for the automated search for the placements of injection and production wells in hot fracture‐controlled reservoirs that sustainably optimize geothermal energy production. We model the reservoirs as discrete fracture networks in 3D. The fluid flow and heat transport in the reservoirs are modeled
Ondřej Pártl, Ernesto Meneses Rioseco
wiley   +1 more source

On an asymptotically linear elliptic Dirichlet problem

Abstract and Applied Analysis, 2002
Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the
Zhitao Zhang, Shujie Li, Shibo Liu, Weijie Feng   +3 more
doaj   +1 more source

Coupled Clustering in Hierarchical Matrices for the Oseen Problem

International Journal for Numerical Methods in Fluids, EarlyView.
Fluid flow problems can be modelled by the Navier‐Stokes or, after linearization, by the Oseen equations. Their discretization results in linear systems in saddle point form which are typically very large and need to be solved iteratively. We propose a novel block structure for hierarchical matrices which is then used to build preconditioners for the ...
Jonas Grams, Sabine Le Borne
wiley   +1 more source

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, EarlyView.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

The non-linear Dirichlet problem and the CR Yamabe problem

Le Matematiche, 1999
See directly the ...
Nicola Garofalo, dimiter Vassilev
doaj  

Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains

, 1984
For D, a bounded Lipschitz domain in Rn, n ⩾ 2, the classical layer potentials for Laplace's equation are shown to be invertible operators on L2(∂D) and various subspaces of L2(∂D).
G. Verchota
semanticscholar   +1 more source