Two-level additive Schwarz methods for discontinuous Galerkin approximations of the biharmonic equation
type: Item
instance of: scholarly article
title: Two-level additive Schwarz methods for discontinuous Galerkin approximations of the biharmonic equation
zbMATH Open document ID: 1385.65063
author: Peng Zhang
published in: Journal of Scientific Computing
publication date: 2018-03-01T00:00:00Z
review text: The paper develops some previous results on two-level nonoverlapping additive Schwarz preconditioners for the symmetric interior penalty Galerkin method formulation, presented by one of the authors in a previous one (2005), namely: adds some numerical experiments and includes in the analysis the important overlapping case for the biharmonic equation.
reviewed by: Constantin Popa
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 35J30
zbMATH DE Number: 6845868
zbMATH Keywords: discontinuous Galerkin methods
zbMATH Keywords: Schwarz methods
zbMATH Keywords: domain decomposition
zbMATH Keywords: preconditioner
zbMATH Keywords: numerical experiments
zbMATH Keywords: biharmonic equation
describes a project that uses: CSparse
MaRDI profile type: Publication
full work available at URL: s10915-017-0453-4
OpenAlex ID: W2615966247
cites work: Q4073917
cites work: An Interior Penalty Finite Element Method with Discontinuous Elements
cites work: Finite Element Methods for Elliptic Equations Using Nonconforming Elements
cites work: Two-level additive Schwarz preconditioners for nonconforming finite element methods
cites work: Poincaré--Friedrichs Inequalities for Piecewise H1 Functions
cites work: \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
cites work: Two-level additive Schwarz preconditioners for \(C^0\) interior penalty methods
cites work: A weakly over-penalized symmetric interior penalty method
cites work: The Mathematical Theory of Finite Element Methods
cites work: A weakly over-penalized symmetric interior penalty method for the biharmonic problem
cites work: Mixed and Hybrid Finite Element Methods
cites work: Q4162607
cites work: Direct Methods for Sparse Linear Systems
cites work: A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
cites work: Q5751903
cites work: Two-Level Additive Schwarz Methods for a Discontinuous Galerkin Approximation of Second Order Elliptic Problems
cites work: Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation
cites work: An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems
cites work: Discontinuous Galerkin methods for the biharmonic problem
cites work: Q4023365
cites work: Two-level additive Schwarz methods for discontinuous Galerkin approximations of second-order elliptic problems
cites work: A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations
cites work: Q4716273
cites work: \(hp\)-version interior penalty DGFEMs for the biharmonic equation
cites work: Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients
cites work: Q4825126
cites work: An Elliptic Collocation-Finite Element Method with Interior Penalties
cites work: Iterative Methods by Space Decomposition and Subspace Correction
cites work: The method of alternating projections and the method of subspace corrections in Hilbert space
cites work: Optimal Solvers for Fourth-Order PDEs Discretized on Unstructured Grids
cites work: Two-Level Schwarz Methods for the Biharmonic Problem Discretized Conforming $C^1 $ Elements
DOI: 10.1007/S10915-017-0453-4
description: scientific article; zbMATH DE number 6845868