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Showing 1 to 20 of 23 for “"A posteriori error estimation"”.
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A variational multiscale a-posteriori error estimation method for nearly incompressible elasticity
This work presents an error estimation framework for a mixed displacement-pressure finite element method for nearly incompressible elasticity that is based on variational multiscale concepts. The displacement field is decomposed into coarse scales captured by the finite element mesh and fine scales …
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Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations
… selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest: the error estimates serve a priori to construct our samples and a posteriori to confirm …
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Reduced basis approximation and a posteriori error estimation for non-coercive elliptic problems : applications to acoustics
… selected points in parameter-time space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide rigorous and sharp bounds for the error in specific outputs of interest; and (iii) offline-online computational procedures - in the offline stage the reduced basis …
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Operator-adapted finite element wavelets : theory and applications to a posteriori error estimation and adaptive computational modeling
We propose a simple and unified approach for a posteriori error estimation and adaptive mesh refinement in finite element analysis using multiresolution signal processing principles. Given a sequence of nested discretizations of a domain we begin by constructing approximation spaces at each level …
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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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Reduced-basis methods applied to problems in elasticity : analysis and applications
… points in parameter space (Accuracy); (ii) a posteriori error estimation - relaxations of the error-residual equation that provide inexpensive bounds for the error in the outputs of interest (Reliability); and (iii) off-line/on-line computational procedures - methods which decouple the …
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Adaptive Finite Element Methods for the Compressible Euler Equations
… quantities of the solution. This includes a posteriori error estimation of the error in the computed quantity as well as adaptive mesh design specifically tailored to the efficient computation of this quantity. We illustrate this approach by several different hyperbolic problems in …
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Adaptive Finite Element Methods for Parameter Identification Problems
… Our approach to this question is based on the a posteriori error estimation for finite element discretization of the problem. We derive a posteriori error estimators to be used in an adaptive mesh refinement algorithm producing economical meshes for parameter identification. The methods developed …
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A Posteriori Error Analysis for a Discontinuous Galerkin Method Applied to Hyperbolic Problems on Tetrahedral Meshes
… we present a simple and efficient \emph{a posteriori} error estimation procedure for a discontinuous finite element method applied to scalar first-order hyperbolic problems on structured and unstructured tetrahedral meshes. We present a local error analysis to derive a discontinuous …
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Reduced basis method for quantum models of crystalline solids
… approximation process; and (iii) inexpensive a posteriori error estimation procedure for outputs of interest. We first propose two strategies by which we can construct efficient reduced basis approximations for vectorial eigensolutions - solutions consisting of several eigenvectors. The first …
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A space-time adaptive method for flows in oil reservoirs
… mesh adaptation is performed based on a posteriori error estimation to reduce the error of a specified output of interest. This work makes use of the DWR method for error estimation and the MOESS algorithm for metric-based mesh optimization. A discontinuous Galerkin finite element …
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Reduced basis method for 2nd order wave equation : application to one-dimensional seismic problem
… computational procedures and the associated a posteriori error estimation are developed. We have shown that the reduced basis pressure distribution is an accurate approximation to the finite element pressure distribution. The greedy algorithm, the procedure of selecting the basis vectors which …
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Reduced-basis output bound methods for parametrized partial differential equations
… properties. Reliability is obtained by a posteriori error estimation methods - relaxations of the standard error-residual equation that provide inexpensive but sharp and rigorous bounds for the error in outputs of interest. Special affine parameter dependence of the differential operator …
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Approximate L² Error Control by Solution Post-Processing for Finite Element Solutions of PDEs with Higher-Order Adaptive Methods
… In this thesis, we build on previous work in a posteriori error estimation and mesh adaptation for finite element methods to propose a new mesh adaptation method based on L² error control by solution post-processing. A key feature of our method is its natural extension to higher-order …
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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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Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification
… (PDEs), and to estimate and control numerical errors via a goal-oriented a posteriori error framework. We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in …
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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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A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems
… cost are included. Additionally, an a posteriori error estimate for the DGM applied to a two-dimensional hyperbolic partial differential equation is constructed. Several examples, both linear and nonlinear, indicating the effectiveness of the error estimate are included.
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