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Showing 1 to 20 of 108 for “"Error estimates"”.
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Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
We study the behavior of truncated Rayleigh-Schröodinger series for the low-lying eigenvalues of the time-independent Schröodinger equation, when the Planck's constant is considered in the semiclassical limit. Under certain hypotheses on the potential energy, we prove that, for any given small …
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Finite volume schemes for hyperbolic-parabolic systems : error estimates
… and of C.Dafermos on the other side, we derive error estimates of the order $O(h^{1/2})$ for finite volume schemes to some hyperbolic--parabolic systems in multi-space dimension. This includes in particular the Euler system with a source term, the compressible Navier--Stokes system and the …
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Error estimates for numerical approximations to scalar conservation laws
… we are concerned with a-priori and a-posteriori error estimates <br>for certain finite volume approximations of scalar hyperbolic conservation laws. <br>We introduce a new technique to prove a-priori error estimates which is based <br>on a duality argument and involves a consistency error of cell …
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A posteriori error estimates and adaptive methods for convection dominated transport processes
In this thesis we derive robust a posteriori error estimates <br>for finite volume approximations of convection dominated nonlinear <br>transport problems. <br>Robustness means that the error estimates are uniform with respect to <br>vanishing diffusion coefficients. <br>The a posteriori error …
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A posteriori error estimates for the Poisson problem on closed, two-dimensional surfaces
… We then construct an adjoint-based a posteriori error estimate for the problem, discuss some computational issues that arise in solving the problem and show some numerical examples. The major sources of numerical error when solving the Poisson problem are geometric error, discretization error, …
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Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces
We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the …
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ERROR ESTIMATES OF NUMERICAL METHODS FOR THE LONG-TIME DYNAMICS OF THE NONLINEAR KLEIN-GORDON EQUATION
This work is devoted to the error estimates of numerical methods for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by $\varepsilon^2$ with $\varepsilon \in (0, 1]$ a dimensionless parameter.The analytical results indicate that …
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A priori analysis of global and local output error estimates for CG, DG and HDG finite element discretizations
In this thesis, a priori convergence estimates are developed for outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for …
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On Numerical Error Estimation for the Finite-Volume Method with an Application to Computational Fluid Dynamics
… each CFD result inherently contains numerical errors that can significantly degrade the accuracy of a simulation. Discretization error is typically the largest contributor to the overall numerical error in a given simulation. Discretization error can be very difficult to estimate since the …
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Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes
… having two outflow edges the finite element error is O(hp+1) superconvergent at the end points of the inflow edge for an augmented space of degree p. Furthermore, we discovered additional mesh-orientation dependent superconvergence points in the interior of triangles. The dependence of these …
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Application of Improved Truncation Error Estimation Techniques to Adjoint Based Error Estimation and Grid Adaptation
… Dynamics (CFD) are subject to discretization error, which is locally generated by truncation error. The discretization error is extremely difficult to properly estimate and this in turn leads to uncertainty over the quality of the numerical solutions obtained via CFD methods and the …
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Analysis of a Spacetime Discontinuous Galerkin Method for Elastodynamics
We prove error estimates for the case of both element-wise and patch-wise causal partitions.
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A Two-Level Method For The Steady-State Quasigeostrophic Equation
… formulation and cite results for optimal error estimates for finding approximate solutions with the finite element method. We examine both the time dependent and steady-state versions of the equations. Numerical experiments verify the error estimates. We examine the Argyris finite element …
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Finite Elements for the Quasi-Geostrophic Equations of the Ocean
… We also, for the first time, develop optimal error estimates for the FE discretization QGE. Numerical tests for the FE discretization and the two-level FE discretization of the QGE are presented and theoretical error estimates are verified. By benchmarking the numerical results against those …
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Parallel and Adaptive Galerkin Methods for Radiative Transfer Problems
… architectures is discussed. A posteriori error estimates allow for efficient grid adaptation in two and three space dimensions.
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Discretization Error Estimation Using the Error Transport Equations for Computational Fluid Dynamics Simulations
… methods, and finite-element methods. Error introduced in the discretization process is called discretization error and defined as the difference between the exact solution to the discrete equations and the exact solution to the partial differential or integral equations. For most CFD …
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A Posteriori Error Analysis of the Discontinuous Galerkin Method for Linear Hyperbolic Systems of Conservation Laws
… for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric and symmetrizable hyperbolic systems of conservation laws. We explicitly write the leading term of the local DG error, which is spanned by Legendre polynomials of degree p and p+1 when p-th …
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Shadowing and numerical analysis of set-valued dynamical systems
… inverse shadowing theorems are proved. Explicit error estimates for the Viability Kernel Algorithm are given for systems which possess the shadowing property.
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On numerical methods for diffusion of electric fields in type-II superconductors
… the convergence of the method, carry out the error estimates and present the numerical experiments. The highlight of Chapter 5 is the generalization of the div-curl lemma. In Chapter 6 we propose a linear iteration scheme to solve a 3D stationary problem. Convergence of the method, error …
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