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Full-Text Articles in Mathematics
Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell
Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell
Theses and Dissertations--Mathematics
In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, …
Lectures On Computational Numerical Analysis Of Partial Differential Equations, James M. Mcdonough
Lectures On Computational Numerical Analysis Of Partial Differential Equations, James M. Mcdonough
Mechanical Engineering Textbook Gallery
From Chapter 1:
The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial differential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity.