A new family of mixed finite elements in IR3
Numerische Mathematik
Mixed finite elements for second order elliptic problems in three variables
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Bending Moment Mixed Method for the Kirchhoff--Love Plate Model
SIAM Journal on Numerical Analysis
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
SIAM Journal on Numerical Analysis
C0 Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains
Journal of Scientific Computing
The Morley element for fourth order elliptic equations in any dimensions
Numerische Mathematik
A Family of ${C}^0$ Finite Elements For Kirchhoff Plates I: Error Analysis
SIAM Journal on Numerical Analysis
Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
Journal of Scientific Computing
A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Journal of Scientific Computing
Computers & Mathematics with Applications
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We introduce a new mixed method for the biharmonic problem. The method is based on a formulation where the biharmonic problem is rewritten as a system of four first-order equations. A hybrid form of the method is introduced which allows us to reduce the globally coupled degrees of freedom to only those associated with Lagrange multipliers which approximate the solution and its derivative at the faces of the triangulation. For $k \ge 1$ a projection of the primal variable error superconverges with order $k+3$ while the error itself converges with order $k+1$ only. This fact is exploited by using local postprocessing techniques that produce new approximations to the primal variable converging with order $k+3$. We provide numerical experiments that validate our theoretical results.