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Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 10/2013, Volume 66, Issue 7, pp. 1245 - 1260
We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several... 
Nonlocal vector calculus | Fractional Laplacian | Finite element methods | Nonlocal diffusion | Fractional Sobolev spaces | Nonlocal operators | MATHEMATICS, APPLIED | TRANSPORT | APPROXIMATION | EQUATIONS | DYNAMICS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 1027 - 1048
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius.... 
Nonlocal operator | Finite elements | Regularity of the solution | Fractional Laplacian | Nonlocal diffusion | Variational inequalities | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDED DOMAINS | DIFFUSION-PROBLEMS | Finite. elements
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2011, Volume 200, Issue 9, pp. 1237 - 1250
In contrast to classical partial differential equation models, the recently developed peridynamic nonlocal continuum model for solid mechanics is an... 
Finite element methods | Peridynamics | Discontinuous Galerkin methods | ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | EQUATION | UNIQUENESS | Finite element method | Models | Analysis | Methods | Differential equations
Journal Article
Computers & Mathematics with Applications, ISSN 0898-1221, 10/2013, Volume 66, Issue 7
We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several... 
Approximation
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 1, pp. 286 - 304
The definition of partial differential equation models usually involves a set of parameters whose values may vary over a wide range. The solution of even a... 
Proper orthogonal decomposition | Reduced-order models | Navier-stokes equations | Ensemble methods | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | RIGHT-HAND SIDES | POD | ensemble methods | ALGORITHM | proper orthogonal decomposition | FLOWS | Navier Stokes equations | reduced-order models | Mathematics
Journal Article
CRYOSPHERE, ISSN 1994-0416, 2013, Volume 7, Issue 1, pp. 19 - 29
The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for... 
ISMIP-HOM | GEOGRAPHY, PHYSICAL | GEOSCIENCES, MULTIDISCIPLINARY | HIGHER-ORDER | APPROXIMATION | DYNAMICS | BENCHMARK EXPERIMENTS | FLOW MODELS | Ice sheets | Usage | Models | Construction | Computational fluid dynamics | Computation | Exact solutions | Fluid flow | Mathematical models | Stokes law (fluid mechanics)
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2007, Volume 196, Issue 45, pp. 4548 - 4560
A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain where fine... 
Atomistic to continuum coupling | Concurrent multiscale | Overlap domain decomposition | atomistic to continuum coupling | DEFECTS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | overlap domain decomposition | concurrent multiscale | MODEL | CRACK | PLASTICITY | Algorithms
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2017, Volume 319, Issue C, pp. 217 - 239
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2014, Volume 52, Issue 1, pp. 243 - 273
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 11/2013, Volume 266, pp. 185 - 204
Journal Article
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, ISSN 0363-0129, 2019, Volume 57, Issue 1, pp. 241 - 263
The optimality system is derived for an optimal control problem governed by a time-fractional PDE. A fully discrete finite element method along with... 
MATHEMATICS, APPLIED | time-fractional equation | finite element method | optimal control | DIFFUSION | convolution quadrature | error estimates | EQUATION | AUTOMATION & CONTROL SYSTEMS
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 07/2019, Volume 351, Issue C, pp. 379 - 403
Journal Article