A residual-baseda posteriori error estimator for the Ciarlet-Raviart formulation of the first biharmonic problem

Abstract

In this article we propose a residual‐based estimator for the psi‐omega formulation of the biharmonic problem. We show how an appropriate modification of Verfürth methodology gives the proper scaling of the residuals leading to both lower and upper estimation. Numerical examples confirm the viability of the method. © 1997 John Wiley & Sons, Inc.

An adaptive least-squares algorithm for the elliptic Monge–Ampère equation

“…On the other hand, the biharmonic problems (10) ( 12) are solved several times within the conjugate gradient algorithm used to solve (8). A posteriori and a priori error estimates for (10) ( 12) can be obtained, but high-order finite element approximations are again needed [33].…”

Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials

“…Lemma 3 (See [34,35]). For bounded interval I and F ∈ H −1 ðIÞ, we set y F as the unique solution of the following homogeneous boundary value problem…”

$hp$-a posteriori error estimates for hybrid high-order methods applied to biharmonic problems

“…C 0 -interior penalty discontinuous Galerkin (IPDG) methods were analyzed in [5] in the quadratic case and in [22] for general order in two space dimensions. Other notable contributions include continuous and discontinuous Galerkin methods for the Kirchhoff-Love plate [25] and the Ciarlet-Raviart formulation of the biharmonic problem [7]. A posteriori error estimates for several lowest-order nonconforming finite element methods applied to biharmonic problems in two and three dimensions are established in [6].…”