Numerical approximation of planar oblique derivative problems in nondivergence form

Dietmar Gallistl
2018 Mathematics of Computation  
A numerical method for approximating a uniformly elliptic oblique derivative problem in two-dimensional simply-connected domains is proposed. The numerical scheme employs a mixed formulation with piecewise affine functions on curved finite element domains. The direct approximation of the gradient of the solution turns the oblique derivative boundary condition into an oblique direction condition. A priori and a posteriori error estimates as well as numerical computations on uniform and adaptive
more » ... iform and adaptive meshes are provided. 2010 Mathematics Subject Classification. 65N12, 65N15, 65N30, Key words and phrases. oblique derivative problem, nondivergence form, Cordes coefficents, a priori error analysis, a posteriori error analysis.
doi:10.1090/mcom/3371 fatcat:up4xgtzolndqxh3ldn2vwgvumu