Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM

Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coeffi-cients Solved by hp-FEM Abstract: In this paper we prove the discrete maximum principle for a one-dimensional equation of the form −(au′) ′ = f with piecewise-constant coeffi-cient a(x), discretized by the hp-FEM. The discrete problem is transformed in such a way that the discontinuity of the coefficient a(x) disappears. Existing results are then applied to obtain a condition on the mesh which guarantees the satisfaction of the discrete maximum principle. Both Dirichlet and mixed Dirichlet-Neumann boundary conditions are discussed