A positivity-preserving Galerkin finite element scheme for a nonlinear reaction-diffusion-advection Mussel-Algal model with Danckwerts boundary conditions

Key Points

• The positivity-preserving scheme effectively simulates a nonlinear reaction-diffusion problem in ecological contexts.
• Significant improvements are seen in model stability and accuracy through the application of the Galerkin finite element approach.
• Numerical analysis of the model showcases robust performance under Danckwerts boundary conditions, ensuring realistic boundary interactions.
• Implications for fisheries management are critical, highlighting the importance of accurate aquatic ecosystem management strategies.