Modified nodal analysisEddy currentsT-omega formulationIn some applications, there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of ...
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-Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one posi...
Based on Lemmas 5.2 and 5.3, we have the following proposition. Proposition 5.4 For any compact set S⊂RN, there exists ε0>0 and C>0 such that for any ε∈(0,ε0) and for any τi∈S there exists a unique ϕε∈K⊥ which solves equation (5.25) and ‖ϕε‖ε≤CεN2+4...
we calculated the nodal points and the corresponding nodal lengths, which were then used to generate the problem’s potential function. Next, we applied the Lipschitz stability approach to demonstrate the stability of the solution. This work contributes to the literature on the inverse SLP by incor...
Based on the constitutive equations ((7), (8), (9)), a natural choice is to take Egq=−kI=EgqI and ɛEɛσ=K. From dimensional analysis, EθR can be chosen in the form EθR=ρctcI=EθRI, where tc is an arbitrary characteristic time and whose choice is discussed in [30...
Birkhoff interpolation Initial value problems Special functions Quadrature rules Error analysis 1. Introduction Let n>1 be a fixed integer. Take a finite system of distinct real nodal points (1)−∞⩽a⩽x1<x2<⋯<xn−1<xn⩽b⩽+∞. We define the matrix (incidence matrix [1]) (...
how to solve problems based on springs? What is the use of multiple pulleys? Do multiple pulleys increase mechanical advantage? If yes, how? How do you calculate the actual mechanical advantage of a lever? How to understand the applications involved in the Physics problems? Explain ...
A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency. The refinement of nodal neighbourhood is accomplished simply by adjusting a scaling factor assigned to control local nodal density. Intensive numerical studies, including the problems with stress ...
many result have been achieved in the study of the nodal set of solution of nonlocal elliptic equation, in particular by using local realisation of the fractional powers of the Laplacian based on the extension technique popularized by the authors in [5]. Also in this setting, the key tools ...