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SIAMNUM
2011

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

10 years 8 months ago
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
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. AMS subject classifications. 65F10, 65F30, 78A30
Pavel B. Bochev, Kara Peterson, Christopher M. Sie
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Where SIAMNUM
Authors Pavel B. Bochev, Kara Peterson, Christopher M. Siefert
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