An a posteriori-driven adaptive mixed high-order method with application to electrostatics

DOI10.1016/j.jcp.2016.08.041zbMath1373.78041OpenAlexW2507532994MaRDI QIDQ1674650

Daniele A. Di Pietro, Ruben Specogna

Publication date: 26 October 2017

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2016.08.041

zbMATH Keywords

electrostaticsa posteriori error analysiscomputational electromagnetismdiscrete geometric approachhybrid high-order methodsvariable diffusiondiscontinuous skeletal methodsmixed high-order methods

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Electro- and magnetostatics (78A30)

Related Items (9)

Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ Convergent adaptive hybrid higher-order schemes for convex minimization ⋮ A Posteriori Error Estimates for Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes ⋮ A posteriori error analysis of the hybrid high-order method for the Stokes problem ⋮ An implicit boundary integral method for computing electric potential of macromolecules in solvent ⋮ Adaptive cell method with constitutive matrix correction for simulating physical field on a coarse grid ⋮ A hybrid high-order discretisation of the Brinkman problem robust in the Darcy and Stokes limits ⋮ Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes ⋮ A discrete de Rham method for the Reissner-Mindlin plate bending problem on polygonal meshes

Uses Software

• Netgen
• ParMGridGen

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics
• On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
• An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
• An aggregation-based algebraic multigrid method
• Mathematical aspects of discontinuous Galerkin methods.
• Computation of stationary 3D halo currents in fusion devices with accuracy control
• An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity
• Generalized HPC method for the Poisson equation
• An optimal Poincaré inequality for convex domains
• A posteriori error estimators for locally conservative methods of nonlinear elliptic problems
• NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
• A note on the Poincaré inequality for convex domains
• Numerical methods in computational electrodynamics. Linear systems in practical applications
• A hybrid high-order locking-free method for linear elasticity on general meshes
• The mathematical structure of classical and relativistic physics. A general classification diagram
• Hybridization of mixed high-order methods on general meshes and application to the Stokes equations
• A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule
• A new set of basis functions for the discrete geometric approach
• Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
• $hp$-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
• Complementary geometric formulations for electrostatics
• A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods
• A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations
• ASYMPTOTIC BEHAVIOUR OF THE ELECTRIC FIELD AND DENSITY OF THE ELECTRIC CHARGE IN THE NEIGHBOURHOOD OF SINGULAR POINTS OF A CONDUCTING SURFACE
• Electrical Impedance Tomography
• A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems
• Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems

This page was built for publication: An a posteriori-driven adaptive mixed high-order method with application to electrostatics