What does this research mean for the field?

A least squares space-time formulation for abstract parabolic equations, solved via a conforming Galerkin discretization of an equivalent saddle point problem, achieves strong convergence and allows for efficient numerical solution without evaluating dual norms. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Develop a symmetric, coercive least-squares space-time framework for abstract parabolic equations under natural regularity assumptions without directly evaluating dual norms.

August 22, 2026Advances in Computational MathematicsOpen Access

A least squares space-time approach for parabolic equations

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Authors

MHMichael Hinze CKChristian Kahle

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Overview

Numerical analysis demonstrates strong convergence and efficient preconditioning for space-time parabolic equations, highlighting robust solver performance.

Key Points

Develop a symmetric, coercive least-squares space-time framework for abstract parabolic equations under natural regularity assumptions without directly evaluating dual norms.
Formulated a least-squares functional in the natural L^2(0,T;V*) x H norm.
Cast the formulation as an equivalent saddle-point problem and applied a conforming Galerkin discretization.
Constructed an efficient preconditioner and verified performance using numerical experiments.
Proved strong convergence of discrete Galerkin solutions toward the continuous analytical solutions.
Eliminated the requirement to directly compute dual V*-norms through the saddle-point reformulation.

Cite This Study

Hinze et al. (2026) studied this question.

synapsesocial.com/papers/6a895e6bca7ade938187c7f3 https://doi.org/10.1007/s10444-026-10345-0

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August 22, 2026Advances in Computational MathematicsOpen Access

A least squares space-time approach for parabolic equations

View Full Paper

Ask AI

Bookmark

Authors

MHMichael Hinze CKChristian Kahle

Discussion

Member takes

Overview

Numerical analysis demonstrates strong convergence and efficient preconditioning for space-time parabolic equations, highlighting robust solver performance.

Key Points

Develop a symmetric, coercive least-squares space-time framework for abstract parabolic equations under natural regularity assumptions without directly evaluating dual norms.
Formulated a least-squares functional in the natural L^2(0,T;V*) x H norm.
Cast the formulation as an equivalent saddle-point problem and applied a conforming Galerkin discretization.
Constructed an efficient preconditioner and verified performance using numerical experiments.
Proved strong convergence of discrete Galerkin solutions toward the continuous analytical solutions.
Eliminated the requirement to directly compute dual V*-norms through the saddle-point reformulation.

Cite This Study

Hinze et al. (2026) studied this question.

synapsesocial.com/papers/6a895e6bca7ade938187c7f3 https://doi.org/10.1007/s10444-026-10345-0

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