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This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value…

Numerical Analysis · Mathematics 2018-10-30 Ulrich Langer , Huidong Yang

This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization…

Numerical Analysis · Mathematics 2021-12-03 Jhuma Sen Gupta

A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We…

Numerical Analysis · Mathematics 2024-11-22 Torsten Linß , Goran Radojev

In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order…

Numerical Analysis · Mathematics 2025-03-13 Thi Thanh Mai Ta , Quang Huy Nguyen , Phi Hung Pham

This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained…

Numerical Analysis · Mathematics 2019-07-08 Robert Altmann , Christoph Zimmer

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…

Numerical Analysis · Mathematics 2022-08-23 Thomas Führer , Michael Karkulik

We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskii spaces and…

Numerical Analysis · Mathematics 2020-04-22 Dominic Breit , Lars Diening , Johannes Storn , Jörn Wichmann

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…

Numerical Analysis · Computer Science 2014-12-19 Petr N. Vabishchevich

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…

Numerical Analysis · Mathematics 2017-08-07 Monika Eisenmann , Eskil Hansen

We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…

Optimization and Control · Mathematics 2014-08-04 Rainer Picard , Sascha Trostorff , Marcus Waurick

This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…

Numerical Analysis · Mathematics 2023-10-30 Jörg Nick

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

We consider a space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation. This variational setting is the starting point for the space-time…

Numerical Analysis · Mathematics 2020-08-06 Ulrich Langer , Marco Zank

We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…

Numerical Analysis · Mathematics 2017-12-05 Bangti Jin , Buyang Li , Zhi Zhou

This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…

Numerical Analysis · Mathematics 2020-04-07 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

Time fractional parabolic problem for p-Laplacian with double singular Hardy-type potential is considered. Comparison principle and appriory estimates for the weak solutions are proved. Existence of global weak solutions and finite-time…

Analysis of PDEs · Mathematics 2026-03-17 Nikolai Kutev , Tsviatko Rangelov

The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…

Numerical Analysis · Mathematics 2022-01-27 Jaeryun Yim , Dongwoo Sheen

Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…

Optimization and Control · Mathematics 2024-10-30 Michael Herty , Kai Hinzmann , Siegfried Müller , Ferdinand Thein

We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…

Optimization and Control · Mathematics 2016-04-27 Michael Hinze , Heiko Kröner

The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…

Numerical Analysis · Mathematics 2022-10-11 Daniel Eckhardt , Barbara Verfürth