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Showing 1 to 11 of 11 for “"Superconvergence"”.
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Superconvergence in Iterated Solutions of Integral Equations
<p>In this thesis, we investigate the superconvergence phenomenon of the iterated numerical solutions for the Fredholm integral equations of the second kind as well as a class of nonliner Hammerstein equations. The term superconvergence was first described in the early 70s in connection with the …
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Superconvergence of Iterated Solutions for Linear and Nonlinear Integral Equations: Wavelet Applications
… Hammerstein equation. We also investigate the superconvergence phenomenon of the iterated Petrov-Galerkin and degenerate kernel numerical solutions of linear and nonlinear integral equations with a class of wavelet basis. The Fredholm integral equations and the Hammerstein equations are …
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Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes
In this thesis, we present new superconvergence properties of discontinuous Galerkin (DG) methods for two-dimensional hyperbolic problems. We investigate the superconvergence properties of the DG method applied to scalar first-order hyperbolic partial differential equations on triangular meshes. We …
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A Posteriori Error Analysis of the Discontinuous Galerkin Method for Linear Hyperbolic Systems of Conservation Laws
… in some cases and establish superconvergence results for some integrals of the error. We develop an efficient implicit residual-based a posteriori error estimation scheme by solving local finite element problems to compute estimates of the leading term of the discretization …
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Singularly perturbed problems with characteristic layers : Supercloseness and postprocessing
… the accuracy of the numerical solution and superconvergence of order (almost) two can be proved. We compare different postprocessing methods and prove superconvergence of above numerical methods on S-type meshes. To recover the exact solution, we apply continuous biquadratic interpolation on …
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A Posteriori Error Analysis for a Discontinuous Galerkin Method Applied to Hyperbolic Problems on Tetrahedral Meshes
… solutions. We investigate pointwise superconvergence properties of the discontinuous Galerkin (DG) method using enriched polynomial spaces. We study the effect of finite element spaces on the superconvergence properties of DG solutions on each class and type of tetrahedral elements. …
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Immersed and Discontinuous Finite Element Methods
In this dissertation we prove the superconvergence of the minimal-dissipation local discontinuous Galerkin method for elliptic problems and construct optimal immersed finite element approximations and discontinuous immersed finite element methods for the Stokes interface problem. In the first part …
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Recovery Techniques For Finite Element Methods And Their Applications
… preserving property, we can able to prove superconvergence of the proposed method on mildly structured meshes. In addition, we establish the ultraconvergence result for the new Hessian recovery technique on translation invariant finite element space of arbitrary order.</p> <p>Our third …
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Dg And Hdg Methods For Curved Structures
… with order k+1 only. Moreover, we show that this superconvergence property does not deteriorate as the thickness of the arch becomes extremely small.</p> <p>Since the DG methods suffer from too many degree of freedoms we introduce and analyze a class of hybridizable</p> <p>discontinuous Galerkin …
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A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation
We propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal convergence rate in the L2- norm. We further show that the q-degree discontinuous solution of a differential equation of order m and its first …