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Elliptic Partial Differential Equations
2016General existence theories for solutions of partial differential equations require using concepts from functional analysis and considering generalizations of classical derivatives based on a multidimensional integration-by-parts formula. The chapter introduces Sobolev spaces, discusses their main properties, states existence theories for elliptic ...
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Elliptic Partial Differential Equations
1984In this chapter we review the main tools used to study elliptic partial differential equations (PDE): Sobolev spaces, variational formulations, and continuous dependence on the data.
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Elliptic partial differential equation and optimal control
Numerical Methods for Partial Differential Equations, 1992AbstractThe theory of optimal control and the semianalytical method of elliptic partial differential equation (PDE) in a prismatic domain are mutually simulated issues. The simulation of discrete‐time linear quadratic (LQ) control with the substructural chain problem in static structural analysis is given first.
Zhong Xiang-Xiang, Zhong Wan-xie
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On solving elliptic stochastic partial differential equations
Computer Methods in Applied Mechanics and Engineering, 2002Abstract A model elliptic boundary value problem of second order, with stochastic coefficients described by the Karhunen–Loeve expansion is addressed. This problem is transformed into an equivalent deterministic one. The perturbation method and the method of successive approximations is analyzed.
Panagiotis Chatzipantelidis +1 more
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Linear Elliptic Partial Differential Equations
2017In earlier chapters, we described how to apply the finite element method to ordinary differential equations. For the remainder of this book, we will focus on extending this technique for application to partial differential equations. As with ordinary differential equations, we begin with a simple example to illustrate the key features.
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Nonlinear Elliptic Partial Differential Equations
2017In Chap. 5, we explained how to apply the finite element method to nonlinear ordinary differential equations. We saw that calculating the finite element solution of nonlinear differential equations required us to solve a nonlinear system of algebraic equations and discussed how these algebraic equations could be solved.
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Coefficient Identification in Elliptic Partial Differential Equation [PDF]
, 2006 We consider the inverse problem for identification of the coefficient in an elliptic partial differential equation inside of the unit square $\mathcal{D}$, when over-posed boundary data are available. Following the main idea of the Method of Variational Imbedding (MVI), we “imbed” the inverse problem into a fourth-order elliptic boundary value problem ...
Christo I. Christov +2 more
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Kernel analysis of elliptic partial differential equations
IBM Systems Journal, 1966The extrapolated Liebmann method for solving partial differential equations is selected for study. With typical computer characteristics in mind, several schemes for organizing the requisite data flow are discussed. To show the potentialities of timing formulas, as well as their limitations and the problems encountered in their construction, one of ...
E. V. Hankam, S. G. Hahn
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On the cibstryctuib of discretizations of elliptic partial differential equations
Journal of Difference Equations and Applications, 1998Algorithmic aspects of a class of finite element collocation methods for the approximate numerical solution of elliptic partial differential equations are described Locall for each finite element the approximate solution is a polynomial. polynomials corresponding toadjacent finite elements need not match continuously but their values and noumal ...
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