## 26 Citations

### Space-time finite element methods for parabolic distributed optimal control problems

- MathematicsArXiv
- 2022

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…

### Least-squares finite elements for distributed optimal control problems

- Computer Science, MathematicsArXiv
- 2022

The proposed method simultaneously solves the state and adjoint equations and is inf – sup stable for any choice of conforming discretization spaces, and a reliable and eﬃcient a posteriori error estimator is derived for problems where box constraints are imposed on the control.

### Space-time virtual elements for the heat equation

- MathematicsArXiv
- 2022

We propose and analyze a space-time virtual element method for the discretization of the heat equation in a space-time cylinder, based on a standard Petrov-Galerkin formulation. Local discrete…

### Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations

- MathematicsIMA Journal of Numerical Analysis
- 2020

Galerkin discretizations of a new well-posed mixed space-time variational formulation of parabolic PDEs are analyzed and the resulting Galerkin operators are shown to be uniformly stable.

### Efficient space‐time adaptivity for parabolic evolution equations using wavelets in time and finite elements in space

- Mathematics, Computer ScienceNumer. Linear Algebra Appl.
- 2023

This work discusses an implementation of the space‐time adaptive method for parabolic evolution equations in which every step is of linear complexity, and derives an algorithm that applies the resulting bilinear forms in linear complexity.

### Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces

- MathematicsSIAM J. Sci. Comput.
- 2021

A space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation and new efficient direct solvers for this system are proposed and investigated.

### A scalable algorithm for solving linear parabolic evolution equations

- Computer Science, MathematicsArXiv
- 2020

An algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space whose solution is a quasi-optimal approximation to the weak solution of the equation at hand is presented.

### A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations

- MathematicsAdvances in Computational Mathematics
- 2022

In this work, an r-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the…

### Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators

- MathematicsComput. Math. Appl.
- 2021

### An Exact Realization of a Modified Hilbert Transformation for Space-Time Methods for Parabolic Evolution Equations

- MathematicsComput. Methods Appl. Math.
- 2021

A new series expansion based on the Legendre chi function to calculate the corresponding matrices for piecewise polynomial functions is introduced, so that the matrix entries for a space-time finite element method for parabolic evolution equations are computable to machine precision independently of the mesh size.

## References

SHOWING 1-10 OF 40 REFERENCES

### Space-Time Finite Element Methods for Parabolic Problems

- Mathematics, Computer ScienceComput. Methods Appl. Math.
- 2015

This approach allows the use of general and unstructured space-time finite elements which do not require any tensor product structure and the stability of the numerical scheme is based on a stability condition which holds for standard finite element spaces.

### Coercive space-time finite element methods for initial boundary value problems

- Mathematics
- 2020

Abstract. We propose and analyse new space-time Galerkin-Bubnov-type finite element formulations of parabolic and hyperbolic second-order partial differential equations in finite time intervals.…

### Space–time hp-approximation of parabolic equations

- MathematicsCalcolo
- 2018

A new space–time finite element method for the solution of parabolic partial differential equations is introduced. In a mesh and degree-dependent norm, it is first shown that the discrete bilinear…

### Space-Time Adaptive Methods for the Mixed Formulation of a Linear Parabolic Problem

- MathematicsJ. Sci. Comput.
- 2018

Numerical results for backward Euler and CN schemes are presented to compare their performance in the time adaptivity setting over uniform/adaptive spatial meshes.

### Least-Squares Galerkin Methods for Parabolic Problems II: The Fully Discrete Case and Adaptive Algorithms

- Computer Science, MathematicsSIAM J. Numer. Anal.
- 2002

This second part of this series on least-squares Galerkin methods for parabolic initial-boundary value problems studies the full discretization in time and space and proves a strengthened Cauchy--Schwarz inequality between coarse and hierarchical surplus space and a bound on the condition number of the auxiliary problem.

### Space-time discretizations using constrained first-order system least squares (CFOSLS)

- Computer ScienceJ. Comput. Phys.
- 2018

### A stable space–time finite element method for parabolic evolution problems

- Mathematics
- 2018

This paper is concerned with the analysis of a new stable space–time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains.…

### New a priori analysis of first‐order system least‐squares finite element methods for parabolic problems

- MathematicsNumerical Methods for Partial Differential Equations
- 2019

We provide new insights into the a priori theory for a time‐stepping scheme based on least‐squares finite element methods for parabolic first‐order systems. The elliptic part of the problem is of…

### Space-time least-squares isogeometric method and efficient solver for parabolic problems

- Computer ScienceMath. Comput.
- 2020

A space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space- time domain and well-suited for parallelization is proposed.

### Least-Squares Galerkin Methods for Parabolic Problems I: Semidiscretization in Time

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2001

The derivation and analysis of one-step methods for semi-discretization in time from least-squares principles for linear parabolic problems with specific combination of piecewise linear, not necessarily continuous, functions with continuous piecewiselinear functions for the flux and scalar variable, respectively.