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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A Nitsche-based nonconforming hp-FE/BE coupling on unstructured non-matching meshes is shown to be stable above an explicit threshold with a priori error estimates for quasi-uniform and geometrically refined discretizations.
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.
A combined linear and nonlinear stabilization for continuous Galerkin finite elements on the transport equation yields localized a priori error bounds of order O(h^{k+1/2}) in the final-time L2 norm under local regularity assumptions.
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
citing papers explorer
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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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Nonconforming $hp$-FE/BE coupling on unstructured meshes based on Nitsche's method
A Nitsche-based nonconforming hp-FE/BE coupling on unstructured non-matching meshes is shown to be stable above an explicit threshold with a priori error estimates for quasi-uniform and geometrically refined discretizations.
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Cut Finite Element Methods for Convection-Diffusion in Mixed-Dimensional Domains
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.
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Local error estimates for a finite element method combining linear and nonlinear stabilization for the linear hyperbolic transport equation
A combined linear and nonlinear stabilization for continuous Galerkin finite elements on the transport equation yields localized a priori error bounds of order O(h^{k+1/2}) in the final-time L2 norm under local regularity assumptions.
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Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.