Summary
The Robin problem for a nonlinear, second-order, elliptic equation is approximated by a primal hybrid method. Optimal order error estimates are established in various norms, with minimal regularity requirements in almost all cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Commun. Pure Appl. Math.12, 623–727 (1959)
Ciarlet, P.G.: The finite element method for elliptic problems. Amsterdam: North Holland 1978
Douglas, J., Jr., Dupont, T.: A Galerkin method for a nonlinear Dirichlet problem. Math. Comp.29, 689–696 (1975)
Douglas, J., Jr., Gupta, C.P., Li, G.: Global estimates for a primal hybrid finite element method for second order elliptic problems in the plane. Mat. Apl. Comput.2, 273–283 (1983)
Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, I. Berlin-Heidelberg-New York: Springer 1972
Milner, F.: Mixed finite element methods for quasilinear second order elliptic problems. Math. Comp.44, 303–320 (1985)
Raviart, P.A., Thomas, J.M.: Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comp.31, 391–413 (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Milner, F.A. A primal hybrid finite element method for quasilinear second order elliptic problems. Numer. Math. 47, 107–122 (1985). https://doi.org/10.1007/BF01389879
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01389879