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Showing 1 to 11 of 11 for “"A posteriori error estimates"”.
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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
… it. 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, …
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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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Parallel and Adaptive Galerkin Methods for Radiative Transfer Problems
… parallel computer architectures is discussed. A posteriori error estimates allow for efficient grid adaptation in two and three space dimensions.
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A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation
… results to construct asymptotically correct a posteriori error estimates. Moreover, we design a new discontinuous Galerkin method to solve the wave equation by using a method of lines approach to separate the space and time where we first apply the classical finite element method using p-degree …
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Error estimates for numerical approximations to scalar conservation laws
… this thesis 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 …
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Adaptive finite elements for viscoelastic deformation problems
… for which we derive optimal order a priori error estimates. We then apply the techniques of the theory of adaptive finite element methods for elliptic boundary value problems and ordinary differential equations, deriving reliable and efficient a posteriori error estimates and detailing …
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An adaptive space-time discontinuous Galerkin method for reservoir flows
… mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual weighted residual method to drive a metric-based mesh optimization algorithm.
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Adaptive Finite Element Methods for Optimization in Partial Differential Equations
A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by (elliptic) partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem …
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Familias paramétricas de procesos iterativos de alto orden de convergencia
… and unique, together with some a priori and a posteriori error estimates. To realize the study of the semilocal convergence of the family, we use two different techniques: the majorant principle and one based in the construction of a system of recurrence relations. In the particular case of …
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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 …