A Discontinuous Galerkin Framework for Efficient Simulation of Cyclic Voltammetry Models
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 $\text{DG}_{\text{Impl}}$, 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 $\text{DG}_{\text{Impl}}$ 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, $\text{DG}_{\text{Impl}}$ 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.