5 papers
An error analysis of discrete Kirchhoff elements
Dietmar Gallistl, Ngoc Tien Tran
The Discrete Kirchhoff Triangle (DKT) method for the biharmonic equation is analyzed in the discrete energy norm. The error is bounded by the best approximation of the Hessian by p…
Quasi-optimal polytopal finite element methods for biharmonic equation
Ngoc Tien Tran
This paper establishes quasi-optimal and lower-order error estimates for weak Galerkin, discontinuous Galerkin, and hybrid-high order finite element methods for the biharmonic equa…
Minimal residual discretization of a class of fully nonlinear elliptic PDE
Dietmar Gallistl, Ngoc Tien Tran
This work introduces finite element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon…
Locking-free hybrid high-order method for linear elasticity
Carsten Carstensen, Ngoc Tien Tran
The hybrid-high order (HHO) scheme has many successful applications including linear elasticity as the first step towards computational solid mechanics. The striking advantage is t…
Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds
Carsten Carstensen, Benedikt Gräßle, Ngoc Tien Tran
The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen, Ern, and Puttkammer [Numer. Math. 149, 2021] require a parameter $C_{\mathrm{…