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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Global estimates for mixed methods for second order elliptic equations

Authors: Jim Douglas and Jean E. Roberts
Journal: Math. Comp. 44 (1985), 39-52
MSC: Primary 65N30
MathSciNet review: 771029
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Abstract: Global error estimates in $ {L^2}(\Omega )$, $ {L^\infty }(\Omega )$, and $ {H^{ - s}}(\Omega )$, $ \Omega $ in $ {{\mathbf{R}}^2}$ or $ {{\mathbf{R}}^3}$, are derived for a mixed finite element method for the Dirichlet problem for the elliptic operator $ Lp = - \operatorname{div}(a\;{\mathbf{grad}}\;p + {\mathbf{b}}p) + cp$ based on the Raviart-Thomas-Nedelec space $ {{\mathbf{V}}_h} \times {W_h} \subset {\mathbf{H}}(\operatorname{div};\Omega ) \times {L^2}(\Omega )$ . Optimal order estimates are obtained for the approximation of p and the associated velocity field $ {\mathbf{u}} = - (a\;{\mathbf{grad}}\;p + {\mathbf{b}}p)$ in $ {L^2}(\Omega )$ and $ {H^{ - s}}(\Omega )$, $ 0 \leqslant s \leqslant k + 1$, and, if $ \Omega \subset {{\mathbf{R}}^2}$ for p in $ {L^\infty }(\Omega )$.

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PII: S 0025-5718(1985)0771029-9
Article copyright: © Copyright 1985 American Mathematical Society

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