The Experts below are selected from a list of 1478562 Experts worldwide ranked by ideXlab platform
Edward Hall - One of the best experts on this subject based on the ideXlab platform.
-
an a posteriori error estimator for hp adaptive discontinuous galerkin methods for elliptic eigenvalue problems
Mathematical Models and Methods in Applied Sciences, 2012Co-Authors: Stefano Giani, Edward HallAbstract:In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded domains in $\mathbb{R}^d$, $d=2,3$, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual based error estimator and use numerical experiments to show that, under an $hp$-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non--smooth eigenfunctions.
Thomas P Wihler - One of the best experts on this subject based on the ideXlab platform.
-
hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems
Journal of Scientific Computing, 2018Co-Authors: Irene Kyza, Stephen Metcalfe, Thomas P WihlerAbstract:This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated.
-
energy norm a posteriori error estimation of hp adaptive discontinuous galerkin methods for elliptic problems
Mathematical Models and Methods in Applied Sciences, 2007Co-Authors: Paul Houston, Dominik Schotzau, Thomas P WihlerAbstract:In this paper, we develop the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders. A series of numerical experiments illustrate the performance of the proposed estimators within an automatic hp-adaptive refinement procedure.
Stefano Giani - One of the best experts on this subject based on the ideXlab platform.
-
A posteriori discontinuous Galerkin error estimator for linear elasticity.
Applied Mathematics and Computation, 2019Co-Authors: Robert E Bird, William M. Coombs, Stefano GianiAbstract:This paper presents for the first time the derivation of an hp a posteriori error estimator for the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis. Any combination of Neumann and Dirichlet boundary conditions are admissible in the formulation, including applying Neumann and Dirichlet on different components on the same region of the boundary. Therefore, the error estimator is applicable to a variety of physical problems. The error estimator is incorporated into an hp-adaptive finite element solver and verified against smooth and non-smooth problems with closed-form analytical solutions, as well as, being demonstrated on a non-smooth problem with complex boundary conditions. The hp-adaptive finite element analyses achieve exponential rates of convergence. The performances of the hp-adaptive scheme are contrasted against uniform and adaptive h refinement. This paper provides a complete framework for adaptivity in the symmetric interior penalty discontinuous Galerkin finite element method for linear elastic analysis.
-
an a posteriori error estimator for hp adaptive discontinuous galerkin methods for elliptic eigenvalue problems
Mathematical Models and Methods in Applied Sciences, 2012Co-Authors: Stefano Giani, Edward HallAbstract:In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded domains in $\mathbb{R}^d$, $d=2,3$, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual based error estimator and use numerical experiments to show that, under an $hp$-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non--smooth eigenfunctions.
Ronald M Levy - One of the best experts on this subject based on the ideXlab platform.
-
the sgb np hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators
Journal of Computational Chemistry, 2002Co-Authors: Emilio Gallicchio, Linda Yu Zhang, Ronald M LevyAbstract:The development and parameterization of a solvent potential of mean force designed to reproduce the hydration thermodynamics of small molecules and macromolecules aimed toward applications in conformation prediction and ligand binding free energy prediction is presented. The model, named SGB/NP, is based on a parameterization of the Surface Generalized Born continuum dielectric electrostatic model using explicit solvent free energy perturbation calculations and a newly developed nonpolar hydration free energy estimator motivated by the results of explicit solvent simulations of the thermodynamics of hydration of hydrocarbons. The nonpolar model contains, in addition to the more commonly used solvent accessible surface area term, a component corresponding to the attractive solute–solvent interactions. This term is found to be important to improve the accuracy of the model, particularly for cyclic and hydrogen bonding compounds. The model is parameterized against the experimental hydration free energies of a set of small organic molecules. The model reproduces the experimental hydration free energies of small organic molecules with an accuracy comparable or superior to similar models employing more computationally demanding estimators and/or a more extensive set of parameters. © 2002 Wiley Periodicals, Inc. J Comput Chem 5: 517–529, 2002; DOI 10.1002/jcc.10045
Paul Houston - One of the best experts on this subject based on the ideXlab platform.
-
energy norm a posteriori error estimation of hp adaptive discontinuous galerkin methods for elliptic problems
Mathematical Models and Methods in Applied Sciences, 2007Co-Authors: Paul Houston, Dominik Schotzau, Thomas P WihlerAbstract:In this paper, we develop the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders. A series of numerical experiments illustrate the performance of the proposed estimators within an automatic hp-adaptive refinement procedure.
