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In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…

Numerical Analysis · Computer Science 2019-11-18 Jesús Bonilla , Santiago Badia

In this paper we propose and investigate a general approach to constructing local energy-preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian PDEs. This approach is based on the temporal…

Numerical Analysis · Mathematics 2021-03-31 Yuwen Li , Xinyuan Wu

In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin…

Numerical Analysis · Mathematics 2025-09-09 Fan Chen , Ming Cui , Chenguang Zhou

Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of…

Numerical Analysis · Mathematics 2021-07-13 Roel Tielen , Matthias Möller , Cornelis Vuik

We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…

Optimization and Control · Mathematics 2023-12-27 Yuqia Wu , Shaohua Pan , Xiaoqi Yang

This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a discretization of linear time-dependent partial differential equation. The core of the method is the multilevel…

Numerical Analysis · Mathematics 2024-01-02 Yogi A. Erlangga

High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to low-order, matrix-based simulations, in particular in porous…

Numerical Analysis · Mathematics 2026-01-06 Christian Engwer , Alexander Schell , Nils-Arne Dreier

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

Methodology · Statistics 2019-01-21 Filip Tronarp , Simo Särkkä

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

Optimization and Control · Mathematics 2013-08-09 Tuğba Akman , Bülent Karasözen

A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a low-rank decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This…

Numerical Analysis · Mathematics 2025-08-25 Andres Galindo-Olarte , Joseph Nakao , Mirjeta Pasha , Jing-Mei Qiu , William Taitano

We first give a general error estimate for the nonconforming approximation of a problem for which a Banach-Ne{\v c}as-Babu{\v s}ka (BNB) inequality holds. This framework covers parabolic problems with general conditions in time (initial…

Numerical Analysis · Mathematics 2023-04-24 Wolfgang Arendt , Isabelle Chalendar , Robert Eymard

In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unknowns…

Numerical Analysis · Mathematics 2017-02-10 Jochen Schütz , David C. Seal , Alexander Jaust

In this paper, we present error estimates of fully discrete Runge--Kutta discontinuous Galerkin (DG) schemes for linear time-dependent partial differential equations. The analysis applies to explicit Runge--Kutta time discretizations of any…

Numerical Analysis · Mathematics 2020-01-07 Zheng Sun , Chi-Wang Shu

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

Numerical Analysis · Mathematics 2020-03-23 Ulrich Langer , Andreas Schafelner

This paper is concerned with the approximation of linear and nonlinearinitial-boundary-value problems of pseudo-parabolic equations with Dirichlet boundary conditions. They are discretized in space by spectral Galerkin and collocation…

Numerical Analysis · Mathematics 2020-02-26 Eduardo Abreu , Angel Durán

We present reliable a posteriori estimators for some fully discrete schemes applied to nonlinear systems of hyperbolic conservation laws in one space dimension with strictly convex entropy. The schemes are based on a method of lines…

Numerical Analysis · Mathematics 2017-09-08 Andreas Dedner , Jan Giesselmann

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…

Numerical Analysis · Mathematics 2018-07-30 Assyr Abdulle , Giacomo Rosilho de Souza

A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…

Numerical Analysis · Mathematics 2025-10-29 Shaoshuai Chu , Michael Herty , Maria Lukacova-Medvidova , Yizhou Zhou

A method is presented for parallelizing the computation of solutions to discrete-time, linear-quadratic, finite-horizon optimal control problems, which we will refer to as LQR problems. This class of problem arises frequently in robotic…

Optimization and Control · Mathematics 2018-09-18 Forrest Laine , Claire Tomlin

In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Benedikt Zeller , Ralf Hiptmair