50 citations · 51 across the 8 of their papers we have counts for
15 papers
Error analysis of penalized -conforming finite element methods for surface Stokes problems
Alan Demlow, Orsan Kilicer
In recent years a number of finite element methods have been developed for the surface Stokes equations. Constructing standard conforming surface finite element methods for the vel…
Alleviating missing boundary conditions in elliptic partial differential equations using interior point measurements
Andrea Bonito, Alan Demlow, Joshua M. Siktar
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measuremen…
A Taylor-Hood finite element method for the surface Stokes problem without penalization
Alan Demlow, Michael Neilan
Finite element approximation of the velocity-pressure formulation of the surfaces Stokes equations is challenging because it is typically not possible to enforce both tangentiality…
A mixed quasi-trace surface finite element method for the Laplace-Beltrami problem
Alan Demlow
Trace finite element methods have become a popular option for solving surface partial differential equations, especially in problems where surface and bulk effects are coupled. In…
A tangential and penalty-free finite element method for the surface Stokes problem
Alan Demlow, Michael Neilan
Surface Stokes and Navier-Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because a…
Maximum norm a posteriori error estimates for convection-diffusion problems
Alan Demlow, Sebastian Franz, Natalia Kopteva
We prove residual-type a posteriori error estimates in the maximum norm for a linear scalar elliptic convection-diffusion problem that may be singularly perturbed. Similar error an…
A divergence-conforming finite element method for the surface Stokes equation
Andrea Bonito, Alan Demlow, Martin Licht
The Stokes equation posed on surfaces is important in some physical models, but its numerical solution poses several challenges not encountered in the corresponding Euclidean setti…
Finite Element Methods for the Laplace-Beltrami Operator
Andrea Bonito, Alan Demlow, Ricardo H. Nochetto
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to t…
A posteriori error estimates for the Laplace-Beltrami operator on parametric surfaces
Andrea Bonito, Alan Demlow
We prove new a posteriori error estimates for surface finite element methods (SFEM). Surface FEM approximate solutions to PDE posed on surfaces. Prototypical examples are elliptic…
A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace-Beltrami Operator
Andrea Bonito, Alan Demlow, Justin Owen
Elliptic partial differential equations on surfaces play an essential role in geometry, relativity theory, phase transitions, materials science, image processing, and other applica…
Convergence and quasi-optimality of adaptive finite element methods for harmonic forms
Alan Demlow
Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electrom…
Convergence and optimality of higher-order adaptive finite element methods for eigenvalue clusters
Andrea Bonito, Alan Demlow
Proofs of convergence of adaptive finite element methods for the approximation of eigenvalues and eigenfunctions of linear elliptic problems have been given in a several recent pap…
A posteriori error estimates for finite element exterior calculus: The de Rham complex
Alan Demlow, Anil N. Hirani
Finite element exterior calculus (FEEC) has been developed over the past decade as a framework for constructing and analyzing stable and accurate numerical methods for partial diff…
Local energy estimates for the finite element method on sharply varying grids
Alan Demlow, Johnny Guzman, Alfred H. Schatz
Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the local energy er…
A posteriori error estimates in the maximum norm for parabolic problems
Alan Demlow, Omar Lakkis, Charalambos Makridakis
We derive a posteriori error estimates in the norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction t…