Skip to content
DraconiticResearch
Search Sources API
184,584 studies31 sourcesUpdated 42 min ago
PreprintCC BY-NC-ND 4.0arXiv

A Discontinuous Galerkin Framework for Efficient Simulation of Cyclic Voltammetry Models

  • Assionvi Hove Kouevi
  • Debora Campos de Faria
  • Can Evren Yarman
  • Gabriel J. Lord
Open at sourcePDFDOICite

Abstract

We develop a numerical framework to efficiently simulate the cyclic voltammetry models based on discontinuous Galerkin (DG) spatial discretization combined with linearly implicit Euler time integration. The method is applied to two electrochemical mechanisms: a heterogeneous electron-transfer (ET) reaction and an electron-transfer reaction coupled with a catalytic chemical step (EC'). The governing time-dependent reaction-diffusion equations are expressed in dimensionless form and discretized in space using locally defined orthonormal Legendre polynomial basis functions. This discretization leads to a system of ordinary differential equations that is subsequently advanced in time using the linearly implicit Euler method. The resulting solver, denoted DGImpl, is evaluated through numerical experiments and compared with MATLAB's pdepe solver in terms of accuracy and computational efficiency. The numerical results demonstrate the convergence of DGImpl with respect to spatial and temporal discretizations and show that the method accurately reproduces the voltammetric responses of both ET and EC' mechanisms. For a prescribed relative error, DGImpl requires less computational time than pdepe in the numerical experiments considered. These results demonstrate the effectiveness of the proposed DG formulation for the forward simulation of cyclic voltammetry models and provide a numerical foundation for subsequent adjoint-based parameter-estimation and inverse-problem formulations.

Related

  1. A discontinuous Petrov-Galerkin finite-element framework for the simulation of microwave-heated flows
    Oreste Marquis, Matthias Maier, Bruno Blais
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingComputational physicsarXiv
  2. A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs
    Andrew Welter, Thea Collin, Ngoc Cuong Nguyen +1
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingFluid dynamicsarXiv
  3. A Novel Matrix-Free Approximate Elemental Inverse for Efficient Preconditioning of Discontinuous Galerkin Spectral Elements
    Boyang Xia, David Moxey
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. An Interface Green's Function Framework for Complete Discrete W1,∞ Analysis of Discontinuous Galerkin Methods
    Haitao Leng, Weifeng Qiu
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  5. A Monolithic Discontinuous Galerkin Framework for Darcy Optimal Control with Radon-Measure Tracking and Pointwise Control Constraints
    SeongHee Jeong, Sanghyun Lee
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{kouevi2026discontinuous,
  title = {{A Discontinuous Galerkin Framework for Efficient Simulation of Cyclic Voltammetry Models}},
  author = {Assionvi Hove Kouevi and Debora Campos de Faria and Can Evren Yarman and Gabriel J. Lord},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04718},
  eprint = {2611.04718},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04718},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A Discontinuous Galerkin Framework for Efficient Simulation of Cyclic Voltammetry Models
AU  - Assionvi Hove Kouevi
AU  - Debora Campos de Faria
AU  - Can Evren Yarman
AU  - Gabriel J. Lord
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04718
UR  - https://arxiv.org/abs/2611.04718
AB  - We develop a numerical framework to efficiently simulate the cyclic voltammetry models based on discontinuous Galerkin (DG) spatial discretization combined with linearly implicit Euler time integration. The method is applied to two electrochemical mechanisms: a heterogeneous electron-transfer (ET) reaction and an electron-transfer reaction coupled with a catalytic chemical step (EC'). The governing time-dependent reaction-diffusion equations are expressed in dimensionless form and discretized in space using locally defined orthonormal Legendre polynomial basis functions. This discretization leads to a system of ordinary differential equations that is subsequently advanced in time using the linearly implicit Euler method. The resulting solver, denoted DG_Impl, is evaluated through numerical experiments and compared with MATLAB's pdepe solver in terms of accuracy and computational efficiency. The numerical results demonstrate the convergence of DG_Impl with respect to spatial and temporal discretizations and show that the method accurately reproduces the voltammetric responses of both ET and EC' mechanisms. For a prescribed relative error, DG_Impl requires less computational time than pdepe in the numerical experiments considered. These results demonstrate the effectiveness of the proposed DG formulation for the forward simulation of cyclic voltammetry models and provide a numerical foundation for subsequent adjoint-based parameter-estimation and inverse-problem formulations.
ER  -