The Discrete Raviart-Thomas Mixed Finite Element Method for the $p$-Laplace Equation

Abstract

We consider the discrete Raviart-Thomas mixed finite element method (dRT-MFEM) for the $p$-Laplace equation in the new sense of measurement. The new measurement of $p$-Laplace equation for $2 ≤ p < ∞$ was studied by D. J. Liu (APPL. NUMER. MATH., 152: 323-337, 2020), where the reliable error analysis for conforming and nonconforming FEM were obtained. This paper provide the reliable and efficient error analysis of dRT-MFEM for $p$-Laplace equation $(1 < p < 2).$ The numerical investigation for benchmark problem demonstrates the accuracy and robustness of the proposed dRT-MFEM.