Silver-based electrochemical memories show enormous potential for non-volatile memory applications. While several groups have made significant strides in device development and process integration, challenges remain to improve function and reliability. The central problem is the large variability of operational parameters and programmed resistance. To understand these variabilities, we need to understand the physics of conducting filament formation and dissolution. Recently, Monte Carlo simulation techniques have been developed to capture the kinetics of Ag transport and metallic filament formation in resistive memory engineered with chalcogenide glass (ChG) films. In this paper the mechanisms of Ag transport and reactions are modeled using a finite element device simulator. The ChG film is modeled as a wide-bandgap semiconductor with material constants (e.g., bandgap, permittivity, electron affinity) extracted from data reported in literature and the results of first principles density functional theory calculations. Active and inert electrodes are modeled as ideal metals with specified workfunctions. The code solves standard carrier statistics and transport equations (continuity, drift-diffusion, and Poisson) and, simultaneously, performs ion transport and reaction calculations. The essential chemistry captured by the simulator are the reduction/oxidation (RedOx) reactions, incorporated as generation (G) and recombination (R) terms in the continuity equations for both ionic and neutral Ag species in the ChG film. The simulation results show how neutral Ag builds up in the film under applied bias. The simulations also reveal that the neutral Ag density is left unchanged once the bias is removed, which enables memristive action. The results provide strong qualitative evidence that finite element codes can simulate ionic transport and metallic growth in ChG-based resistive memory. Quantitative comparisons to experimental data will be provided in the final paper.