Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 49, Issue 1, Pages 159-181Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090772095
Keywords
least-squares finite element methods; div-curl boundary value problem; face elements; edge elements; compatible discretizations
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Funding
- U.S. Department of Energy's National Nuclear Security Administration [DE-AC04-94AL85000]
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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.
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