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

• DOI: 10.1137/090772095
• Publication Date: 2011-02-08T23:11:58Z
• Authors: Pavel B. Bochev; Kara Peterson; Christopher M. Si...
• Keywords: Curl (programming language); Multigrid method; Least-squares function approximation

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 vector field on is solved using curl-conforming elements. second problem specifies normal handled by div-conforming prove that both formulations are norm-equivalent with respect to suitable discrete norms, yield optimal asymptotic error estimates, give rise algebraic systems can be efficient multigrid methods. Numerical results illustrate scalability iterative solvers rates convergence also included.