Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations

Authors:
Pavel B. Bochev;Kara Peterson;Christopher M. Siefert
Affiliations:
pbboche@sandia.gov and kjpeter@sandia.gov;-;csiefer@sandia.gov
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 23
Cited 0

A new family of mixed finite elements in IR3

Numerische Mathematik
Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
Direct discretization of planar div-curl problems

SIAM Journal on Numerical Analysis
Adjoint operators for the natural discretizations of the divergence gradient and curl on logically rectangular grids

Applied Numerical Mathematics
Covolume Solutions of Three-Dimensional Div-Curl Equations

SIAM Journal on Numerical Analysis
Multigrid Method for Maxwell's Equations

SIAM Journal on Numerical Analysis
Mimetic discretizations for Maxwell's equations

Journal of Computational Physics
An Aggregation-Based Domain Decomposition Preconditioner for Groundwater Flow

SIAM Journal on Scientific Computing
First-Order System $\CL\CL^*$ (FOSLL*): Scalar Elliptic Partial Differential Equations

SIAM Journal on Numerical Analysis
The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem

SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Parallel multigrid smoothing: polynomial versus Gauss--Seidel

Journal of Computational Physics
Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I

SIAM Journal on Numerical Analysis
Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part II

SIAM Journal on Numerical Analysis
An overview of the Trilinos project

ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An Improved Convergence Bound for Aggregation-Based Domain Decomposition Preconditioners

SIAM Journal on Matrix Analysis and Applications
First-Order System LL* (FOSLL*) for General Scalar Elliptic Problems in the Plane

SIAM Journal on Numerical Analysis
Weighted-Norm First-Order System Least Squares (FOSLS) for Problems with Corner Singularities

SIAM Journal on Numerical Analysis
FOSLL* Method for the Eddy Current Problem with Three-Dimensional Edge Singularities

SIAM Journal on Numerical Analysis
An estimator for the diagonal of a matrix

Applied Numerical Mathematics
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces

SIAM Journal on Numerical Analysis
A Weighted $H(div)$ Least-Squares Method for Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis
An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We develop and analyze least-squares finite element methods for two complementary div-curl elliptic boundary value problems. The first one prescribes the tangential component of the vector field on the boundary and is solved using curl-conforming elements. The second problem specifies the normal component of the vector field and is handled by div-conforming elements. We prove that both least-squares formulations are norm-equivalent with respect to suitable discrete norms, yield optimal asymptotic error estimates, and give rise to algebraic systems that can be solved by efficient algebraic multigrid methods. Numerical results that illustrate scalability of iterative solvers and optimal rates of convergence are also included.