| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2837 - 2861 | |
| DOI | https://doi.org/10.1051/m2an/2025077 | |
| Published online | 24 October 2025 | |
hp-error analysis of a continuous Petrov–Galerkin time-stepping scheme for linear parabolic equations
Department of Mathematics, Shanghai Normal University, Shanghai 200234, P.R. China
* Corresponding author: ylj5152@shnu.edu.cn
Received:
28
June
2025
Accepted:
9
September
2025
We present a fully discrete hp-version numerical method for second-order linear parabolic equations, combining a continuous Petrov–Galerkin (CPG) time-stepping scheme with a standard continuous Galerkin (CG) finite element method in space. Our analysis provides a priori error estimates in the L2(L2)- and L∞(L2)-norms, where all constants are fully robust – independent of temporal and spatial discretization parameters. For solutions with initial singularities at t = 0, exponential temporal convergence is achieved through geometrically graded time meshes and linearly increasing polynomial degrees. Numerical experiments confirm the theoretical convergence rates.
Mathematics Subject Classification: 65M60 / 65M12 / 65M15
Key words: Parabolic equations / hp-version continuous Petrov–Galerkin method / time-stepping scheme / exponential convergence / initial singularity
© The authors. Published by EDP Sciences, SMAI 2025
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