Numerical analysis of stochastic Stefan problem using gradient discretisation method

This thesis investigates the numerical approximation of stochastic Stefan problems (SSPs) with multiplicative noise, emphasizing convergence analysis, implementation, and efficient solvers. Using the Gradient Discretisation Method (GDM), convergence was rigorously proven, and a weak martingale solution established, applicable to various numerical methods. The gradient scheme was implemented with P1 finite elements and HMM methods. To address computational challenges, efficient linearised and regularised solvers were introduced, reusing pre-computed matrices to reduce Jacobian overhead in the Newton method. Sensitivity analyses and adaptive tolerances further enhanced solver efficiency and performance.