Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
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Establishes equivalence of DEC cochains with generalized Whitney forms to prove convergence rates for the Hodge-Laplacian in full k-form generality on well-centered meshes.
A structure-preserving upwind DG scheme with convex splitting for the Cahn-Hilliard-Darcy tumor growth model that maintains mass conservation, pointwise bounds, and a discrete energy law.
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
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A nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity techniques and applications to nonlinear PDEs
Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
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A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms
Establishes equivalence of DEC cochains with generalized Whitney forms to prove convergence rates for the Hodge-Laplacian in full k-form generality on well-centered meshes.
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Structure-preserving upwind DG scheme for a Cahn-Hilliard-Darcy model of tumor growth
A structure-preserving upwind DG scheme with convex splitting for the Cahn-Hilliard-Darcy tumor growth model that maintains mass conservation, pointwise bounds, and a discrete energy law.
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On a linear DG approximation of chemotaxis models with damping gradient nonlinearities
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.