Results 281 to 290 of about 456,102 (333)

Elliptic Partial Differential Equations

2018
Let us consider the three-dimensional regular domain \(D\subset R^3\) bounded by the Liapunov surface \(S=\partial D\). In the classical mathematical analysis the following formula is proved which is called the Gauss-Ostrogradski-Green’s formula.
Andreas Öchsner, Marin Marin
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On Elliptic Partial Differential Equations [PDF]

open access: possible, 2011
This series of lectures will touch on a number of topics in the theory of elliptic differential equations. In Lecture I we discuss the fundamental solution for equations with constant coefficients. Lecture 2 is concerned with Calculus inequalities including the well known ones of Sobolev. In lectures 3 and 4 we present the Hilbert space approach to the
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Applications to Elliptic Partial Differential Equations [PDF]

open access: possible, 2012
We consider elliptic partial differential equations in d variables and their discretisation in a product grid \(\mathbf{I} = \times^{d}_{j=1}I_{j}\). The solution of the discrete system is a grid function, which can directly be viewed as a tensor in \(\mathbf{V} = {\bigotimes}^{d}_{j=1}\mathbb{K}^{I_{j}}\). In Sect.
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Partial differential equations I — elliptic equations [PDF]

open access: possible, 1986
In this chapter we start to examine some techniques used for the numerical solution of partial differential equations (PDEs) and, in particular, equations which are special cases of the linear second-order equation with two independent variables $$a\frac{{{\partial ^2}u}}{{\partial {x^2}}} + b\frac{{{\partial ^2}u}}{{\partial x\partial y}} + c\frac{
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Partial Differential Equations of Elliptic Type

Physics Bulletin, 1971
C Miranda Berlin: Springer 1970 pp xii + 370 price DM 58 This is a translation of the second revised edition of the monograph published in 1955. The number of pages has risen from 222 to 370 of which 69 are occupied by a bibliography.
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Partial Differential Equations of Elliptic Type

2004
In the present chapter we consider the well-posedness of an abstract boundary-value problem for differential equations of elliptic type $$- \upsilon ''\left( t \right) + A\upsilon \left( t \right) = f\left( t \right)\left( {0 \leqslant t \leqslant T} \right),\upsilon \left( 0 \right) = {{\upsilon }_{0}},\upsilon \left( T \right) = {{\upsilon }_{T}}$$
Pavel E. Sobolevskii   +1 more
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Multilevel Schwarz methods for elliptic partial differential equations

Computer Methods in Applied Mechanics and Engineering, 2011
We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstructured mesh partitions and with subdomain boundaries resulting from using the mesh partitioner.
Alfio Quarteroni   +2 more
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