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This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary condition in the three dimensional…

Numerical Analysis · Mathematics 2012-12-11 Xiaobing Feng , Haijun Wu

In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the…

Numerical Analysis · Mathematics 2017-07-20 Hui Guo , Yang Yang

In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…

Numerical Analysis · Mathematics 2026-05-28 Ruo Li , Qicheng Liu , Fanyi Yang , Shuhai Zhao

The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…

Optimization and Control · Mathematics 2024-07-15 Ahmad Mousavi , George Michailidis

Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a restricted additive method for the Poisson equation and write a…

Numerical Analysis · Mathematics 2023-04-19 Juan Galvis

We use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation. The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with…

Numerical Analysis · Mathematics 2021-03-24 Evan North , Semyon Tsynkov , Eli Turkel

We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…

Optimization and Control · Mathematics 2016-01-12 Madeleine Udell , Stephen Boyd

We consider one-level additive Schwarz domain decomposition preconditioners for the Helmholtz equation with variable coefficients (modelling wave propagation in heterogeneous media), subject to boundary conditions that include wave…

Numerical Analysis · Mathematics 2020-10-06 Shihua Gong , Ivan G. Graham , Euan A. Spence

We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…

Numerical Analysis · Mathematics 2023-07-07 Sander Rhebergen , Garth N. Wells

We revisit the L2 norm error estimate for the C0 interior penalty analysis of fourth order Dirichlet boundary control problem. The L2 norm estimate for the optimal control is derived under reduced regularity assumption and this analysis can…

Optimization and Control · Mathematics 2022-10-18 Sudipto Chowdhury , Divay Garg , Ravina Shokeen

We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formulation of the problem, and deliver $O(h^{k+1})$ $H^2$-error…

Numerical Analysis · Mathematics 2022-04-11 Zhaonan Dong , Alexandre Ern

A mathematical analysis is presented for a class of interior penalty (IP) discontinuous Galerkin approximations of elliptic boundary value problems. In the framework of the present theory one can derive some overpenalized IP bilinear forms…

Numerical Analysis · Mathematics 2014-09-11 Ferenc Izsák

A novel overlapping domain decomposition splitting algorithm based on a Crank-Nisolson method is developed for the stochastic nonlinear Schroedinger equation driven by a multiplicative noise with non-periodic boundary conditions. The…

Numerical Analysis · Mathematics 2023-09-08 Lihai Ji

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that…

Numerical Analysis · Mathematics 2015-03-11 Michael Dumbser , Olindo Zanotti , Raphael Loubere , Steven Diot

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

Optimization and Control · Mathematics 2026-02-24 Zhendong Li , Akwum Onwunta , Bedřich Sousedík

Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling…

Numerical Analysis · Mathematics 2023-06-28 Juan G. Calvo , Juan Galvis

We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter…

Numerical Analysis · Mathematics 2024-06-14 Sijing Liu , Valeria Simoncini

We develop an a posteriori analysis of C^0 interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C^0 interior penalty methods for…

Numerical Analysis · Mathematics 2017-12-21 Susanne C. Brenner , Joscha Gedicke , Li-yeng Sung , Yi Zhang

In this paper, we propose a two-level block preconditioned Jacobi-Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of $2m$th ($m = 1, 2$) order symmetric elliptic…

Numerical Analysis · Mathematics 2023-04-13 Qigang Liang , Wei Wang , Xuejun Xu

In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth order problem into a system of second order equations.…

Numerical Analysis · Mathematics 2025-09-30 Hengguang Li , Peimeng Yin