Develops a model-independent energy-based CutFEM formulation for finite-strain elasticity using automatic differentiation, with cut-independent stability analysis and convergence results for both smooth solutions and corner singularities.
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Hybrid sharp-diffuse interface finite element method for accurate thermo-hydrodynamic modeling of melt pools with rapid evaporation.
Develops explicit IFE functions and an IDG method for elliptic interface problems that achieve optimal H1 and L2 convergence with interface-cut-independent constants and robust matrix conditioning.
DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.
A shifted interface method is extended to transient poroelasticity, enabling first-order accurate modeling of embedded cracks on unfitted meshes with weak or strong interface enforcement.
A CutFEM is developed and analyzed for convection-diffusion on hierarchical mixed-dimensional manifolds, with a priori error estimates in energy and L2 norms that hold for reduced regularity solutions.
Non-conformal immersed and union-based isogeometric methods with boundary-conformal quadrature reduce patch count and preprocessing for magnetostatics while union variants maintain accuracy on benchmarks.
A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.
Block preconditioner with velocity-pressure Schur approximation yields mesh-independent GMRES convergence for SBM-Stokes via field-of-values analysis showing non-symmetric terms are small perturbations on fine meshes.
Parameter regimes and symmetric monotonic positive initial data ensure positivity for all time and pointwise convergence to a constant steady state outside the origin in a diffusion model with Dirac reaction term, via Laplace transform arguments.
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Positivity and long-term behaviour of a diffusion model with measure-valued nonlocal reaction term
Parameter regimes and symmetric monotonic positive initial data ensure positivity for all time and pointwise convergence to a constant steady state outside the origin in a diffusion model with Dirac reaction term, via Laplace transform arguments.