Two simple finite element methods for Reissner--Mindlin plates with clamped boundary condition

TL;DR

This paper introduces two straightforward finite element methods using mortar techniques for discretizing Reissner--Mindlin plates with clamped boundaries, providing proven optimal error estimates.

Contribution

The paper proposes novel finite element methods based on mortar techniques specifically for clamped Reissner--Mindlin plates, with rigorous error analysis.

Findings

Both methods achieve optimal a priori error estimates.

The methods are simple to implement for clamped boundary conditions.

The approach extends mortar finite element techniques to plate problems.

Abstract

We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite element techniques. We prove optimal a priori error estimates for both methods.