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Volume 22, Issue 4
An Unconditionally Energy-Stable SAV-DG Numerical Scheme for Tumor Growth Model

Penghao Guo, Bo Wang & Guang-An Zou

DOI: 10.4208/ijnam2025-1022

Int. J. Numer. Anal. Mod., 22 (2025), pp. 510-533.

Published online: 2025-04

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  • Abstract

In this paper, we propose a linear, fully decoupled and unconditionally energy-stable discontinuous Galerkin (DG) method for solving the tumor growth model, which is derived from the variation of the free energy. The fully discrete scheme is constructed by the scalar auxiliary variable (SAV) for handling the nonlinear term and backward Euler method for the time discretization. We rigorously prove the unconditional energy stability and optimal error estimates of the scheme. Finally, several numerical experiments are performed to verify the energy stability and validity of the proposed scheme.

  • Keywords

Tumor growth model, DG method, SAV approach, optimal error estimates.

  • AMS Subject Headings

35Q35, 65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-22-510, author = {Guo , PenghaoWang , Bo and Zou , Guang-An}, title = {An Unconditionally Energy-Stable SAV-DG Numerical Scheme for Tumor Growth Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {4}, pages = {510--533}, abstract = {

In this paper, we propose a linear, fully decoupled and unconditionally energy-stable discontinuous Galerkin (DG) method for solving the tumor growth model, which is derived from the variation of the free energy. The fully discrete scheme is constructed by the scalar auxiliary variable (SAV) for handling the nonlinear term and backward Euler method for the time discretization. We rigorously prove the unconditional energy stability and optimal error estimates of the scheme. Finally, several numerical experiments are performed to verify the energy stability and validity of the proposed scheme.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1022}, url = {http://global-sci.org/intro/article_detail/ijnam/24038.html} }
TY - JOUR T1 - An Unconditionally Energy-Stable SAV-DG Numerical Scheme for Tumor Growth Model AU - Guo , Penghao AU - Wang , Bo AU - Zou , Guang-An JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 510 EP - 533 PY - 2025 DA - 2025/04 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1022 UR - https://global-sci.org/intro/article_detail/ijnam/24038.html KW - Tumor growth model, DG method, SAV approach, optimal error estimates. AB -

In this paper, we propose a linear, fully decoupled and unconditionally energy-stable discontinuous Galerkin (DG) method for solving the tumor growth model, which is derived from the variation of the free energy. The fully discrete scheme is constructed by the scalar auxiliary variable (SAV) for handling the nonlinear term and backward Euler method for the time discretization. We rigorously prove the unconditional energy stability and optimal error estimates of the scheme. Finally, several numerical experiments are performed to verify the energy stability and validity of the proposed scheme.

Guo , PenghaoWang , Bo and Zou , Guang-An. (2025). An Unconditionally Energy-Stable SAV-DG Numerical Scheme for Tumor Growth Model. International Journal of Numerical Analysis and Modeling. 22 (4). 510-533. doi:10.4208/ijnam2025-1022
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