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A posteriori error estimates in finite element methods for general Friedrichs' systems
Computer Methods in Applied Mechanics and Engineering, 2000The authors give a new a posteriori error estimator for the general Friedrichs system based on a comparison of an appropriate norm of the exact error with an approximate solution. The estimate is independent of space dimension and the method of numerical approximation.
Jacques Baranger +3 more
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Friedrichs Method in a Lyapunov Problem
Applicable Analysis, 2002By using the well-known Friedrichs extension and some a priori inequality, we obtain weak solutions of a Lyapunov equation. In particular, we show that the Lyapunov functions satisfying necessary and sufficient conditions in the domain of asymptotic stability of a singular point some dynamical system must be absolutely continuous.
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A Unified Discontinuous Petrov--Galerkin Method and Its Analysis for Friedrichs' Systems
SIAM Journal on Numerical Analysis, 2013We propose a unified discontinuous Petrov--Galerkin (DPG) framework with optimal test functions for Friedrichs-like systems, which embrace a large class of elliptic, parabolic, and hyperbolic partial differential equations (PDEs). The well-posedness, i.e., existence, uniqueness, and stability, of the DPG solution is established on a single abstract DPG
Tan Bui-Thanh +2 more
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Lax–Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws [PDF]
Journal of Computational Physics, 2013 Fast sweeping methods are efficient iterative numerical schemes originally designed for solving stationary Hamilton-Jacobi equations. Their efficiency relies on Gauss-Seidel type nonlinear iterations, and a finite number of sweeping directions. In this paper, we generalize the fast sweeping methods to hyperbolic conservation laws with source terms. The
Weitao Chen +2 more
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Quasinilpotent variant of Friedrichs' method in the theory of similarity of linear operators
Functional Analysis and Its Applications, 1984Let X denote a complex Banach space. A closed linear operator A on X is called non-quasianalytic, if it has a representation \(A=A_ 1+iA_ 2\), \(D(A)\subset D(A_ 1)\cap D(A_ 2)\), where \(iA_ 1\), \(iA_ 2\), are generators of strongly continuous groups of operators \(\{T_ 1(t)\}\), \(\{T_ 2(t)\}\), \(t\geq 0\), which commute, and \(\int (\log \| T_ k(t)
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Petroleum Science and Technology, 2013
The authors present a system model of partial differential equations concerning the variation of the pressure and temperature at different time and depth in high temperature-high pressure (HTHP) gas wells. Finite difference methods with Lax-Friedrichs scheme are improved to solve this set of conservation equations. The basic data of X Well (HTHP well),
Zhiguo Qiao +5 more
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The authors present a system model of partial differential equations concerning the variation of the pressure and temperature at different time and depth in high temperature-high pressure (HTHP) gas wells. Finite difference methods with Lax-Friedrichs scheme are improved to solve this set of conservation equations. The basic data of X Well (HTHP well),
Zhiguo Qiao +5 more
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Nonlinear Analysis: Theory, Methods & Applications, 1992
The author continues his study of the solvable Friedrichs extension of a densely defined nonlinear, unbounded, and \(K\)-strongly stable operator initiated in [Ill. J. Math. 10, 255--274 (1966; Zbl 0139.31503)]. The abstract results are illustrated by applications to the diffusion equation \[ -\Delta u+g(x)\frac{\partial u}{\partial y}+f(u,y)=h(x,y ...
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The author continues his study of the solvable Friedrichs extension of a densely defined nonlinear, unbounded, and \(K\)-strongly stable operator initiated in [Ill. J. Math. 10, 255--274 (1966; Zbl 0139.31503)]. The abstract results are illustrated by applications to the diffusion equation \[ -\Delta u+g(x)\frac{\partial u}{\partial y}+f(u,y)=h(x,y ...
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2015
In his lecture On the Different Methods of Translating Friedrich Schleiermacher distinguishes two different ways of translating: either the translator moves the reader to the author or the translator moves the author to the reader. Thus, for Schleiermacher the goal of translation lies in the approximation of two persons and in enabling interpersonal ...
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In his lecture On the Different Methods of Translating Friedrich Schleiermacher distinguishes two different ways of translating: either the translator moves the reader to the author or the translator moves the author to the reader. Thus, for Schleiermacher the goal of translation lies in the approximation of two persons and in enabling interpersonal ...
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Convergence of the finite volume method for Friedrichs' systems
Summary: This note is devoted to the derivation of an error estimate in ``\(h^{1/2}\)'' of the finite volume approximation of Friedrichs' systems. Our proof makes no use of finite elements techniques, and so applies to both explicit and implicit schemes.Vila, Jean-Paul, Villedieu, Philippe
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Convergence of renormalized particle methods for Friedrichs systems
zbMATH Open Web Interface contents unavailable due to conflicting licenses.Lanson, Nathalie, Vila, Jean-Paul
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