Results 341 to 350 of about 685,179 (397)

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, Allaberen Ashyralyev   +1 more
openaire   +2 more sources

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, Alfio Quarteroni, Giovanni Migliorati   +2 more
openaire   +4 more sources

Elliptic Partial Differential Equations

2016
General 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

1984
In 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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Approaching A Partial Differential Equation Of Mixed Elliptic-Hyperbolic Type

, 2002
We discuss a quasilinear second-order partial differential equation of mixed elliptic-hyperbolic type in two independent variables, which originates from a certain fully nonlinear system of first order partial differential equations.
R. Magnaninf, G. Talenti
semanticscholar   +1 more source

On solving elliptic stochastic partial differential equations

Computer Methods in Applied Mechanics and Engineering, 2002
Abstract 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, Ivo Babuška   +1 more
openaire   +2 more sources

Optimal Control of Quasilinear $\boldsymbol{H}(\mathbf{curl})$-Elliptic Partial Differential Equations in Magnetostatic Field Problems

SIAM Journal of Control and Optimization, 2013
This paper examines the mathematical and numerical analysis for optimal control problems governed by quasilinear $\boldsymbol{H}(\mathbf{curl})$-elliptic partial differential equations.
Irwin Yousept
semanticscholar   +1 more source

Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients

SIAM Journal on Numerical Analysis, 2012
We consider the problem of numerically approximating the solution of an elliptic partial differential equation with random coefficients and homogeneous Dirichlet boundary conditions.
J. Charrier
semanticscholar   +1 more source

Linear Elliptic Partial Differential Equations

2017
In 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, 2004
We 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
semanticscholar   +1 more source