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SIAM Journal on Scientific Computing, ISSN 1064-8275, 2013, Volume 35, Issue 6, pp. A2752 - A2780
... EQUATIONS ERIK BURMAN Abstract. In this paper we propose a new method to stabilize nonsymmetric indenite problems. The idea is to solve a forward and an adjoint problem... 
Noncoercive problems | Continuous interior penalty | Compressible flow | Cauchy problem | Galerkin least squares | Stabilized finite element methods | continuous interior penalty | MATHEMATICS, APPLIED | APPROXIMATION | compressible flow | stabilized finite element methods | CAUCHY-PROBLEM | noncoercive problems
Journal Article
SIAM journal on numerical analysis, ISSN 0036-1429, 01/2019, Volume 57, Issue 6, pp. 2785 - 2811
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2017, Volume 86, Issue 303, pp. 75 - 96
In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. The recently derived framework from... 
MATHEMATICS, APPLIED | SOLVE | QUASI-REVERSIBILITY METHOD | APPROXIMATION | REGULARIZATION
Journal Article
Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2015, Volume 288, pp. 2 - 23
Journal Article
International journal for numerical methods in engineering, ISSN 0029-5981, 2015, Volume 104, Issue 7, pp. 472 - 501
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 11/2015, Volume 49, pp. 141 - 146
We propose a simple upwind finite element method that is monotonicity preserving and weakly consistent of order O(h32). The scheme is nonlinear, but since an... 
Transport equation | Stabilized finite element method | Monotonicity preserving | Shock capturing | Flux correction | MATHEMATICS, APPLIED | DISCRETE MAXIMUM PRINCIPLE
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 04/2017, Volume 355, Issue 4, pp. 479 - 484
In this note, we prove error estimates in natural norms on the approximation of the boundary data in the elliptic Cauchy problem, for the finite element method... 
MATHEMATICS | FINITE-ELEMENT METHODS
Journal Article
Applied numerical mathematics, ISSN 0168-9274, 2012, Volume 62, Issue 4, pp. 328 - 341
We extend the classical Nitsche type weak boundary conditions to a fictitious domain setting. An additional penalty term, acting on the jumps of the gradients... 
Interior penalty | Fictitious domain | Finite element | MATHEMATICS, APPLIED | Finite element method | Methods | Mathematical analysis | Upper bounds | Boundary conditions | Mathematical models | Boundaries | Estimates | Optimization | Mathematics | Matematik
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 07/2014, Volume 352, Issue 7-8, pp. 655 - 659
We propose an analysis for the stabilized finite element methods proposed in Burman (2013) [2] valid in the case of ill-posed problems for which only weak... 
MATHEMATICS | Finite element method | Analysis | Methods | Magnetic properties
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 10/2015, Volume 25, Issue 11, pp. 2015 - 2042
We propose an error analysis for a shock capturing finite element method for the Burgers' equation using the duality theory due to Tadmor. The estimates use a... 
shock capturing | stabilized finite element method | Burgers' equation | error estimates | CONVECTION-DIFFUSION EQUATIONS | MATHEMATICS, APPLIED | SPECTRAL VISCOSITY APPROXIMATIONS | SCALAR CONSERVATION-LAWS | CONVERGENCE | MONOTONE-DIFFERENCE APPROXIMATIONS | SCHEMES
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 12/2014, Volume 24, Issue 13, pp. 2663 - 2684
We consider transient convection-diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field... 
Convection-diffusion | Passive transport | Stabilized finite element method | Error estimates | stabilized finite element method | MATHEMATICS, APPLIED | STABILIZATION | CONVECTION | FINITE-ELEMENT METHODS | EQUATIONS | GALERKIN APPROXIMATIONS | error estimates | convection-diffusion
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2014, Volume 36, Issue 4, pp. A1911 - A1936
In this paper we consider stabilized finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of... 
Noncoercive problems | Hyperbolic equations | Finite elements | Transport | Stabilization | MATHEMATICS, APPLIED | hyperbolic equations | stabilization | APPROXIMATIONS | CONVECTION | DISCONTINUOUS GALERKIN METHODS | transport | noncoercive problems | finite elements
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 01/2008, Volume 24, Issue 1, pp. 127 - 143
Journal Article
Numerische Mathematik, ISSN 0029-599X, 7/2018, Volume 139, Issue 3, pp. 505 - 528
... element methods Erik Burman 1 · Lauri Oksanen 1 Received: 23 September 2016 / Revised: 16 November 2017 / Published online: 10 February 2018 © The Author(s) 2018... 
65M15 | Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | 65M30 | Mathematics | Numerical and Computational Physics, Simulation | 65M12 | 65M32 | REGULARIZATION | MATHEMATICS, APPLIED | Finite element method | Usage | Analysis | Methods
Journal Article
ESAIM. Mathematical modelling and numerical analysis, ISSN 1290-3841, 2019, Volume 52, Issue 6, pp. 2247 - 2282
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 03/2014, Volume 30, Issue 2, pp. 567 - 592
Projection stabilization applied to general Lagrange multiplier finite element methods is introduced and analyzed in an framework. We then consider some... 
stabilized finite element method | Lagrange multiplier method | Nitsche's method | MATHEMATICS, APPLIED | FINITE-ELEMENT-METHOD | STOKES | Boundaries
Journal Article
Numerische Mathematik, ISSN 0029-599X, 03/2020, Volume 144, Issue 3, pp. 451 - 477
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2018, Volume 87, Issue 311, pp. 1029 - 1050
We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes equations. The method uses a... 
STOKES EQUATIONS | MATHEMATICS, APPLIED
Journal Article
Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2010, Volume 199, Issue 41-44, pp. 2680 - 2686
We propose a fictitious domain method where the mesh is cut by the boundary. The primal solution is computed only up to the boundary; the solution itself is... 
Interior penalty | Fictitious domain | Finite element | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | BOUNDARY | Finite element method | Methods | Multipliers | Lagrange multipliers | Mathematical analysis | Mathematical models | Boundaries | Optimization | Convergence | Beräkningsmatematik | Computational Mathematics
Journal Article
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