Results 51 to 60 of about 18,335 (312)
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,\
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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 +3 more
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Infinite dimension of solutions of the Dirichlet problem
Open Mathematics, 2015 It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
Ryazanov Vladimir
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A Mathematical Model for Two‐Phase Flow in Confined Environments: Numerical Solution and Validation
International Journal for Numerical Methods in Fluids, EarlyView.We present a numerical framework based on the Cahn‐Hilliard‐Navier‐Stokes (CHNS) model to simulate biphasic flow in confined environments. After deriving the mathematical model, we develop the weak form of the system of PDEs using a pedagogical approach to enable its implementation in FEniCS.
Giuseppe Sciumè +3 more
wiley +1 more source
International Journal for Numerical Methods in Fluids, EarlyView.The proposed work implements a direct flux reconstruction method for spatial discretization and a stiffness‐resilient exponential time integration method for temporal discretization on the cube‐sphere grid. A space‐time tensor formalism is employed to provide a general representation in any curvilinear coordinate system. This combination enables highly
Stéphane Gaudreault +6 more
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International Journal for Numerical Methods in Fluids, EarlyView.This paper presents a finite element method for simulating highly viscoelastic flows of pure polymer melts using the Elastic Viscous Stress Splitting formulation. The method avoids higher‐order derivatives in the weak formulation by reformulating the convective term in the constitutive equation.
R. Ahmad, P. Zajac, S. Turek
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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 +3 more
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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 +3 more
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On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems [PDF]
, 2021 Pier Domenico Lamberti, Luigi Provenzano
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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
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