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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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Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
SIAM Journal on Numerical Analysis, 2012We consider the problem of numerically approximating the solution of an elliptic partial differential equation with random coefficients and homogeneous Dirichlet boundary conditions.
J. Charrier
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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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Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis, 2004We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions.
I. Babuska, R. Tempone, G. E. Zouraris
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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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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 nonlinear elliptic partial differential equations and hölder continuity
, 19531. This paper is concerned with genera! nonlinear elliptic partial differential equations of second order for functions of two independent variables. New a priori estimates for the derivatives of solutions of such equations are derived and used to obtain
L. Nirenberg
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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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The Computational Complexity of Elliptic Partial Differential Equations
1972In this paper, we consider the computational complexity of the class of all procedures for computing a second order accurate approximation (on a square grid) to the solution of a linear, second order elliptic partial differential equation in a square domain.
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