65 citations · 111 across the 22 of their papers we have counts for
27 papers
The transposition method in saddle-point problems
Dietmar Gallistl, Zhen Liu
The transposition method known from the theory of second-order elliptic partial differential equations is formulated for saddle-point problems under certain structural assumptions…
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…
A posteriori error estimates for a modified Morley FEM
A. K. Dond, D. Gallistl, S. Nayak +1
Residual-based a~posteriori error estimators are derived for the modified Morley FEM, proposed by Wang, Xu, Hu [J. Comput. Math, 24(2), 2006], for the singularly perturbed biharmon…
The Adini finite element on locally refined meshes
Dietmar Gallistl
This work introduces a locally refined version of the Adini finite element for the planar biharmonic equation on rectangular partitions with at most one hanging node per edge. If g…
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…
Mixed finite elements for the Gross-Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound
Dietmar Gallistl, Moritz Hauck, Yizhou Liang +1
We establish an a priori error analysis for the lowest-order Raviart-Thomas finite element discretisation of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence…
Mixed methods and lower eigenvalue bounds
Dietmar Gallistl
It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue b…
A posteriori error estimates for nonconforming discretizations of singularly perturbed biharmonic operators
Dietmar Gallistl, Shudan Tian
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite…
Localized implicit time stepping for the wave equation
Dietmar Gallistl, Roland Maier
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subpr…
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 $…
Computational multiscale methods for nondivergence-form elliptic partial differential equations
Philip Freese, Dietmar Gallistl, Daniel Peterseim +1
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients sat…
Continuous finite elements satisfying a strong discrete Miranda--Talenti identity
Dietmar Gallistl, Shudan Tian
This article introduces continuous -nonconforming finite elements in two and three space dimensions which satisfy a strong discrete Miranda--Talenti inequality in the sense th…
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…
Computational lower bounds of the Maxwell eigenvalues
Dietmar Gallistl, Vladislav Olkhovskiy
A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi…
Mixed finite element approximation of periodic Hamilton--Jacobi--Bellman problems with application to numerical homogenization
Dietmar Gallistl, Timo Sprekeler, Endre Süli
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-…
Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements
Kaifang Liu, Dietmar Gallistl, Matthias Schlottbom +1
An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented…
A priori error analysis of a numerical stochastic homogenization method
Julian Fischer, Dietmar Gallistl, Daniel Peterseim
This paper provides an a~priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem.…
Numerical homogenization of H(curl)-problems
Dietmar Gallistl, Patrick Henning, Barbara Verfürth
If an elliptic differential operator associated with an -problem involves rough (rapidly varying) coefficients, then solutions to the corresponding $\mat…
Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM
C. Carstensen, D. Gallistl, J. Gedicke
This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise…
Numerical stochastic homogenization by quasilocal effective diffusion tensors
Dietmar Gallistl, Daniel Peterseim
This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective determin…
Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wavenumber Explicit Bounds
Donald L. Brown, Dietmar Gallistl
The simulation of the elastodynamics equations at high-frequency suffers from the well known pollution effect. We present a Petrov--Galerkin multiscale sub-grid correction method t…
Computation of quasilocal effective diffusion tensors and connections to the mathematical theory of homogenization
Dietmar Gallistl, Daniel Peterseim
This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of Målqvist and Peterseim [Math. Comp. 2014], which…
Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients
Dietmar Gallistl
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formul…
Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations
Donald L. Brown, Dietmar Gallistl, Daniel Peterseim
This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime.…