Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis
Ruchi Guo
Abstract
Immersed finite element (IFE) methods are a group of long-existing numerical methods for solving interface problems on unfitted meshes. A core argument of the methods is to avoid a mesh regeneration procedure when solving moving interface problems. Despite the various applications in moving interface problems, a complete theoretical study on the convergence behavior is still missing. This research is devoted to closing the gap between numerical experiments and theory. We present the first fully discrete analysis including the stability and optimal error estimates for a backward Euler IFE method for solving parabolic moving interface problems. Numerical results are also presented to validate the analysis.
Topics & Concepts
Polygon meshInterface (matter)Convergence (economics)MathematicsFinite element methodStability (learning theory)Numerical analysisEuler's formulaClosing (real estate)Applied mathematicsBackward Euler methodNumerical stabilityMathematical optimizationComputer scienceMathematical analysisEuler equationsGeometryBubbleMachine learningPolitical scienceParallel computingLawThermodynamicsPhysicsMaximum bubble pressure methodEconomicsEconomic growthAdvanced Numerical Methods in Computational MathematicsLattice Boltzmann Simulation StudiesComputational Fluid Dynamics and Aerodynamics