12 citations · 38 across the 11 of their papers we have counts for
11 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{…
Discrete weak duality of hybrid high-order methods for convex minimization problems
Ngoc Tien Tran
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex…
Finite element approximation for uniformly elliptic linear PDE of second order in nondivergence form
Ngoc Tien Tran
This paper proposes a novel technique for the approximation of strong solutions to uniformly elliptic linear PDE of second order…
Stability and guaranteed error control of approximations to the Monge--Ampère equation
Dietmar Gallistl, Ngoc Tien Tran
This paper analyzes a regularization scheme of the Monge--Ampère equation by uniformly elliptic Hamilton--Jacobi--Bellman equations. The main tools are stability estimates in the $…
Stabilization-free HHO a posteriori error control
Fleurianne Bertrand, Carsten Carstensen, Benedikt Gräßle +1
The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an effici…
Convergence of a regularized finite element discretization of the two-dimensional Monge-Ampère equation
Dietmar Gallistl, Ngoc Tien Tran
This paper proposes a regularization of the Monge-Ampère equation in planar convex domains through uniformly elliptic Hamilton-Jacobi-Bellman equations. The regularized problem pos…
Convergent adaptive hybrid higher-order schemes for convex minimization
Carsten Carstensen, Ngoc Tien Tran
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the…