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Numerische Mathematik, ISSN 0029-599X, 03/2016, Volume 132, Issue 3, pp. 519 - 539
This paper characterizes the norm of the residual of mixed schemes in their natural functional framework with fluxes or stresses in H(div) and displacements in... 
65N15 | 65N12 | 65N30 | ELASTICITY | EQUATIONS | MATHEMATICS, APPLIED | UNIFYING THEORY
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1572 - 1607
Journal Article
Numerische Mathematik, ISSN 0029-599X, 12/2017, Volume 137, Issue 4, pp. 857 - 893
Journal Article
Journal of computational methods in applied mathematics, ISSN 1609-9389, 2019, Volume 20, Issue 3, pp. 437 - 458
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear... 
Linear Scalar Hyperbolic Equation | Gradient Discretisation Method | 65N12 | Numerical Tests | Convergence Analysis | 65N30
Journal Article
Numerische Mathematik, ISSN 0029-599X, 09/2016, Volume 134, Issue 1, pp. 197 - 222
A novel residual-type a posteriori error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or... 
65N15 | 76S05 | 65N12 | 65N30 | 65N06 | MATHEMATICS, APPLIED | CONVERGENCE | APPROXIMATIONS | DISCRETIZATIONS | Finite element method | Analysis | Methods
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2016, Volume 309, pp. 579 - 609
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with... 
Adaptivity | DPG | Linear elasticity | Variational formulations | Minimum residual method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | WEAKLY IMPOSED SYMMETRY | FINITE-ELEMENT METHODS | EQUATIONS | Mathematics - Numerical Analysis
Journal Article
Numerische Mathematik, ISSN 0029-599X, 5/2019, Volume 142, Issue 1, pp. 1 - 32
We generalize the two dimensional mixed finite elements of Arbogast and Correa (SIAM J Numer Anal 54:3332–3356, 2016) defined on quadrilaterals to three... 
Mathematical Methods in Physics | 65N12 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 41A10 | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 65N30
Journal Article
Numerische Mathematik, ISSN 0945-3245, 2019, Volume 143, Issue 1, pp. 139 - 175
An explicit and computable error estimator for the $$hp$$ hp version of the virtual element method (VEM), together with lower and upper bounds with respect to... 
Mathematical Methods in Physics | 65N12 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 65N30 | MATHEMATICS, APPLIED | MATHEMATICS AND COMPUTING
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 12/2016, Volume 354, Issue 12, pp. 1236 - 1240
In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability... 
MATHEMATICS
Journal Article
Numerische Mathematik, ISSN 0029-599X, 6/2016, Volume 133, Issue 2, pp. 203 - 231
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $$L^2$$ L... 
65N15 | Mathematical Methods in Physics | 65N12 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65N30 | Finite element method | Mechanical engineering | Analysis | Methods
Journal Article
Numerische Mathematik, ISSN 0945-3245, 2016, Volume 135, Issue 3, pp. 711 - 732
Journal Article
Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2016, Volume 309, pp. 497 - 531
Journal Article
Numerische Mathematik, ISSN 0029-599X, 7/2019, Volume 142, Issue 3, pp. 749 - 786
We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resulting... 
65N15 | Mathematical Methods in Physics | 65N12 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 74B10 | 65N30 | MATHEMATICS, APPLIED
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 09/2016, Volume 80, pp. 1 - 23
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized... 
Holonomic ansatz | Finite element method | Holonomic function | Inverse inequality | Zeilberger's algorithm | Symbolic determinant evaluation | 68W30 | 65N12 | 15A45 | MSC primary 33F10 | 05A20 | 65F15 | 15A15 | secondary 65N30 | MATHEMATICS, APPLIED | FINITE-ELEMENTS | COMPUTER ALGEBRA | PROOF | Analysis | Research institutes
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 09/2018, Volume 25, Issue 3, pp. 337 - 348
In the present work the Cauchy problem for an abstract evolution equation with a Lipschitz-continuous operator is considered, where the main operator... 
65M15 | 65N12 | quasi-linear evolution equation | operator splitting | 65N22 | Decomposition scheme | MATHEMATICS
Journal Article
Calcolo, ISSN 1126-5434, 2018, Volume 55, Issue 1, pp. 1 - 23
Some error analyses on virtual element methods (VEMs) including inverse inequalities, norm equivalence, and interpolation error estimates are developed for... 
Inverse inequality | 65N12 | Interpolation error estimate | Numerical Analysis | Virtual elements | Mathematics | Theory of Computation | Norm equivalence | 65N30 | MATHEMATICS | MATHEMATICS, APPLIED | 2ND-ORDER ELLIPTIC PROBLEMS | SPACES | DISCONTINUOUS GALERKIN METHOD
Journal Article