Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence. - Erik Burman; Alexandre Ern (Math. Comput., 2005)

A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty. - Erik Burman (SIAM J. Numer. Anal., 2005)

Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method. - Malte Braack; Erik Burman (SIAM J. Numer. Anal., 2006)

Continuous Interior Penalty Finite Element Method for Oseen's Equations. - Erik Burman; Miguel A. Fernández; Peter Hansbo (SIAM J. Numer. Anal., 2006)

A Domain Decomposition Method Based on Weighted Interior Penalties for Advection-Diffusion-Reaction Problems. - Erik Burman; Paolo Zunino (SIAM J. Numer. Anal., 2006)

Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems. - Erik Burman; Benjamin Stamm (J. Sci. Comput., 2007)

Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. - Erik Burman; Alexandre Ern (Math. Comput., 2007)

Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence. - Erik Burman; Miguel A. Fernández (Numerische Mathematik, 2007)

Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Transient Stokes Equations: Stability and Convergence Analysis. - Erik Burman; Miguel A. Fernández (SIAM J. Numer. Anal., 2008)

Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems. - Erik Burman; Benjamin Stamm (SIAM J. Numer. Anal., 2008)

A Continuous Interior Penalty Method for Viscoelastic Flows. - Andrea Bonito; Erik Burman (SIAM J. Sci. Comput., 2008)

A Posteriori Error Estimation for Interior Penalty Finite Element Approximations of the Advection-Reaction Equation. - Erik Burman (SIAM J. Numer. Anal., 2009)

Interior Penalty Continuous and Discontinuous Finite Element Approximations of Hyperbolic Equations. - Erik Burman; Alfio Quarteroni; Benjamin Stamm (J. Sci. Comput., 2010)

Bubble stabilized discontinuous Galerkin method for parabolic and elliptic problems. - Erik Burman; Benjamin Stamm (Numerische Mathematik, 2010)

Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems. - Erik Burman; Alexandre Ern; Miguel A. Fernández (SIAM J. Numer. Anal., 2010)

Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages. - Malte Braack; Erik Burman; Nico Taschenberger (SIAM J. Sci. Comput., 2011)

A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions. - Erik Burman (SIAM J. Numer. Anal., 2012)

Stabilized Finite Element Methods for Nonsymmetric, Noncoercive, and Ill-Posed Problems. Part I: Elliptic Equations. - Erik Burman (SIAM J. Sci. Comput., 2013)

Stabilized Finite Element Methods for Nonsymmetric, Noncoercive, and Ill-Posed Problems. Part II: Hyperbolic Equations. - Erik Burman (SIAM J. Sci. Comput., 2014)

A monotonicity preserving, nonlinear, finite element upwind method for the transport equation. - Erik Burman (Appl. Math. Lett., 2015)

A Stabilized Cut Finite Element Method for the Three Field Stokes Problem. - Erik Burman; Susanne Claus; André Massing (SIAM J. Sci. Comput., 2015)

A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization. - Pierre Cantin; Jérôme Bonelle; Erik Burman; Alexandre Ern (Comput. Math. Appl., 2016)

Cut finite element methods for coupled bulk-surface problems. - Erik Burman; Peter Hansbo; Mats G. Larson; Sara Zahedi (Numerische Mathematik, 2016)

Local CIP Stabilization for Composite Finite Elements. - Erik Burman; Friedhelm Schieweck (SIAM J. Numer. Anal., 2016)

Software frameworks for integral equations in electromagnetic scattering based on Calderón identities. - Matthew W. Scroggs; Timo Betcke; Erik Burman; Wojciech Smigaj; Elwin van't Wout (Comput. Math. Appl., 2017)

Error estimates for transport problems with high Péclet number using a continuous dependence assumption. - Erik Burman; Isaac P. Santos (J. Comput. Appl. Math., 2017)

A stabilized nonconforming finite element method for the elliptic Cauchy problem. - Erik Burman (Math. Comput., 2017)

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes. - Gabriel R. Barrenechea; Erik Burman; Fotini Karakatsani (Numerische Mathematik, 2017)

The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem. - Erik Burman; Peter Hansbo; Mats G. Larson (SIAM J. Numer. Anal., 2017)

A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces. - Erik Burman; Peter Hansbo; Mats G. Larson; André Massing; Sara Zahedi (CoRR, 2018)

Fictitious domain method with boundary value correction using penalty-free Nitsche method. - Thomas Boiveau; Erik Burman; Susanne Claus; Mats G. Larson (J. Num. Math., 2018)

Stabilized nonconforming finite element methods for data assimilation in incompressible flows. - Erik Burman; Peter Hansbo (Math. Comput., 2018)

A cut finite element method with boundary value correction. - Erik Burman; Peter Hansbo; Mats G. Larson (Math. Comput., 2018)

Data assimilation for the heat equation using stabilized finite element methods. - Erik Burman; Lauri Oksanen (Numerische Mathematik, 2018)

An Unfitted Hybrid High-Order Method for Elliptic Interface Problems. - Erik Burman; Alexandre Ern (SIAM J. Numer. Anal., 2018)

Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem. - Erik Burman; Mats G. Larson; Lauri Oksanen (SIAM J. Numer. Anal., 2018)

The Unfitted HHO Method for the Stokes Problem on Curved Domains. - Erik Burman; Guillaume Delay; Alexandre Ern (ENUMATH, 2019)

3D-2D Stokes-Darcy Coupling for the Modelling of Seepage with an Application to Fluid-Structure Interaction with Contact. - Erik Burman; Miguel A. Fernández; Stefan Frei; Fannie M. Gerosa (ENUMATH, 2019)

Augmented Lagrangian Method for Thin Plates with Signorini Boundaries. - Erik Burman; Peter Hansbo; Mats G. Larson (ENUMATH, 2019)

A Posteriori Error Estimates with Boundary Correction for a Cut Finite Element Method. - Erik Burman; Cuiyu He; Mats G. Larson (CoRR, 2019)

L2-Error estimates for H(div)-conforming schemes applied to a linearised model of inviscid incompressible flow. - Gabriel R. Barrenechea; Erik Burman; Johnny Guzmán (CoRR, 2019)

Stability and error analysis of a splitting method using Robin-Robin coupling applied to a fluid-structure interaction problem. - Erik Burman; Rebecca Durst; Johnny Guzmán (CoRR, 2019)

Space time stabilized finite element methods for a unique continuation problem subject to the wave equation. - Erik Burman; Ali Feizmohammadi; Arnaud Münch; Lauri Oksanen (CoRR, 2019)

Finite element approximation of the Laplace-Beltrami operator on a surface with boundary. - Erik Burman; Peter Hansbo; Mats G. Larson; Karl Larsson 001; André Massing (Numerische Mathematik, 2019)

Stabilized CutFEM for the convection problem on surfaces. - Erik Burman; Peter Hansbo; Mats G. Larson; Sara Zahedi (Numerische Mathematik, 2019)

Primal Dual Mixed Finite Element Methods for Indefinite Advection-Diffusion Equations. - Erik Burman; Cuiyu He (SIAM J. Numer. Anal., 2019)

Boundary Element Methods with Weakly Imposed Boundary Conditions. - Timo Betcke; Erik Burman; Matthew W. Scroggs (SIAM J. Sci. Comput., 2019)

Hybridized CutFEM for Elliptic Interface Problems. - Erik Burman; Daniel Elfverson; Peter Hansbo; Mats G. Larson; Karl Larsson 001 (SIAM J. Sci. Comput., 2019)

Cut Bogner-Fox-Schmit elements for plates. - Erik Burman; Peter Hansbo; Mats G. Larson (Adv. Model. Simul. Eng. Sci., 2020)

Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics. - Erik Burman; Snorre Christiansen; Peter Hansbo (CoRR, 2020)

Stability estimate for scalar image velocimetry. - Erik Burman; J. J. J. Gillissen; Lauri Oksanen (CoRR, 2020)

Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty. - Erik Burman; Johnny Guzmán (CoRR, 2020)

A finite element data assimilation method for the wave equation. - Erik Burman; Ali Feizmohammadi; Lauri Oksanen (Math. Comput., 2020)

A cut finite element method for a model of pressure in fractured media. - Erik Burman; Peter Hansbo; Mats G. Larson (Numerische Mathematik, 2020)

A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime. - Erik Burman; Mihai Nechita; Lauri Oksanen (Numerische Mathematik, 2020)

A Fully Discrete Numerical Control Method for the Wave Equation. - Erik Burman; Ali Feizmohammadi; Lauri Oksanen (SIAM J. Control. Optim., 2020)

Weak Imposition of Signorini Boundary Conditions on the Boundary Element Method. - Erik Burman; Stefan Frei; Matthew W. Scroggs (SIAM J. Numer. Anal., 2020)

Error estimates for the Smagorinsky turbulence model: enhanced stability through scale separation and numerical stabilization. - Erik Burman; Peter Hansbo; Mats G. Larson (CoRR, 2021)

A mechanically consistent model for fluid-structure interactions with contact including seepage. - Erik Burman; Miguel A. Fernández; Stefan Frei; Fannie M. Gerosa (CoRR, 2021)

Weighted error estimates for transient transport problems discretized using continuous finite elements with interior penalty stabilization on the gradient jumps. - Erik Burman (CoRR, 2021)

Spacetime finite element methods for control problems subject to the wave equation. - Erik Burman; Ali Feizmohammadi; Arnaud Münch; Lauri Oksanen (CoRR, 2021)

Convergence Analysis of Hybrid High-Order Methods for the Wave Equation. - Erik Burman; Omar Durán; Alexandre Ern; Morgane Steins (J. Sci. Comput., 2021)

Comparison of Shape Derivatives Using CutFEM for Ill-posed Bernoulli Free Boundary Problem. - Erik Burman; Cuiyu He; Mats G. Larson (J. Sci. Comput., 2021)

A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation. - Naveed Ahmed 004; Gabriel R. Barrenechea; Erik Burman; Johnny Guzmán; Alexander Linke; Christian Merdon (SIAM J. Numer. Anal., 2021)

A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation. - Erik Burman; Guillaume Delay; Alexandre Ern (SIAM J. Numer. Anal., 2021)

An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems. - Erik Burman; Matteo Cicuttin; Guillaume Delay; Alexandre Ern (SIAM J. Sci. Comput., 2021)

On the Design of Locking Free Ghost Penalty Stabilization and the Relation to CutFEM with Discrete Extension. - Erik Burman; Peter Hansbo; Mats G. Larson (CoRR, 2022)

Continuous Interior Penalty stabilization for divergence-free finite element methods. - Gabriel R. Barrenechea; Erik Burman; Ernesto Cáceres; Johnny Guzmán (CoRR, 2022)

Extension Operators for Trimmed Spline Spaces. - Erik Burman; Peter Hansbo; Mats G. Larson; Karl Larsson 001 (CoRR, 2022)

The augmented Lagrangian method as a framework for stabilised methods in computational mechanics. - Erik Burman; Peter Hansbo; Mats G. Larson (CoRR, 2022)

Cut finite element method for divergence free approximation of incompressible flow: optimal error estimates and pressure independence. - Erik Burman; Peter Hansbo; Mats G. Larson (CoRR, 2022)

Unique continuation for the Lamé system using stabilized finite element methods. - Erik Burman; Janosch Preuß (CoRR, 2022)

Two mixed finite element formulations for the weak imposition of the Neumann boundary conditions for the Darcy flow. - Erik Burman; Riccardo Puppi (J. Num. Math., 2022)

Hybrid coupling of finite element and boundary element methods using Nitsche's method and the Calderon projection. - Timo Betcke; Michal Bosy; Erik Burman (Numer. Algorithms, 2022)

Fully discrete loosely coupled Robin-Robin scheme for incompressible fluid-structure interaction: stability and error analysis. - Erik Burman; Rebecca Durst; Miguel A. Fernández; Johnny Guzmán (Numerische Mathematik, 2022)

Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains. - Erik Burman; Stefan Frei; André Massing (Numerische Mathematik, 2022)

CutFEM based on extended finite element spaces. - Erik Burman; Peter Hansbo; Mats G. Larson (Numerische Mathematik, 2022)

A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime. - Erik Burman; Mihai Nechita; Lauri Oksanen (Numerische Mathematik, 2022)

An A Posteriori Error Estimate of the Outer Normal Derivative Using Dual Weights. - Silvia Bertoluzza; Erik Burman; Cuiyu He (SIAM J. Numer. Anal., 2022)

Boundary Element Methods for Helmholtz Problems With Weakly Imposed Boundary Conditions. - Timo Betcke; Erik Burman; Matthew W. Scroggs (SIAM J. Sci. Comput., 2022)

Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension. - Erik Burman; Peter Hansbo; Mats G. Larson (SIAM J. Sci. Comput., 2022)

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation. - Erik Burman; Deepika Garg; Janosch Preuß (CoRR, 2023)

A primal dual mixed finite element method for inverse identification of the diffusion coefficient and its relation to the Kohn-Vogelius penalty method. - Erik Burman (CoRR, 2023)

Finite element approximation of unique continuation of functions with finite dimensional trace. - Erik Burman; Lauri Oksanen (CoRR, 2023)

Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs. - Silvia Bertoluzza; Erik Burman; Cuiyu He (CoRR, 2023)

Unique continuation for an elliptic interface problem using unfitted isoparametric finite elements. - Erik Burman; Janosch Preuß (CoRR, 2023)

Optimal finite element approximation of unique continuation. - Erik Burman; Mihai Nechita; Lauri Oksanen (CoRR, 2023)

An abstract framework for heterogeneous coupling: stability, approximation and applications. - Silvia Bertoluzza; Erik Burman (CoRR, 2023)

Loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling: Unified analysis for parabolic/parabolic and parabolic/hyperbolic problems. - Erik Burman; Rebecca Durst; Miguel A. Fernández; Johnny Guzmán (J. Num. Math., 2023)

Some Observations on the Interaction Between Linear and Nonlinear Stabilization for Continuous Finite Element Methods Applied to Hyperbolic Conservation Laws. - Erik Burman (SIAM J. Sci. Comput., 2023)

Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation. - Michal Bosy; Matthew W. Scroggs; Timo Betcke; Erik Burman; Christopher D. Cooper (J. Comput. Chem., 2023)

Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions. - Erik Burman; Peter Hansbo; Mats G. Larson (Math. Comput., 2023)

The Unique Continuation Problem for the Heat Equation Discretized with a High-Order Space-Time Nonconforming Method. - Erik Burman; Guillaume Delay; Alexandre Ern (SIAM J. Numer. Anal., 2023)

Implicit-Explicit Time Discretization for Oseen's Equation at High Reynolds Number with Application to Fractional Step Methods. - Erik Burman; Deepika Garg; Johnny Guzmán (SIAM J. Numer. Anal., 2023)

Computational unique continuation with finite dimensional Neumann trace. - Erik Burman; Lauri Oksanen; Ziyao Zhao (CoRR, 2024)

Attached and separated rotating flow over a finite height ridge. - Stefan Frei; Erik Burman; Edward R. Johnson (CoRR, 2024)

Solving the unique continuation problem for Schrödinger equations with low regularity solutions using a stabilized finite element method. - Erik Burman; Mingfei Lu; Lauri Oksanen (CoRR, 2024)

A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems. - Erik Burman; Rebecca Durst; Miguel A. Fernández; Johnny Guzmán; Sijing Liu (CoRR, 2024)

Unique continuation for the wave equation based on a discontinuous Galerkin time discretization. - Erik Burman; Janosch Preuß (CoRR, 2024)

Implicit-explicit Crank-Nicolson scheme for Oseen's equation at high Reynolds number. - Erik Burman; Deepika Garg; Johnny Guzmán (CoRR, 2024)

On inf-sup stability and optimal convergence of the quasi-reversibility method for unique continuation subject to Poisson's equation. - Erik Burman; Mingfei Lu (CoRR, 2024)

Stabilizing and Solving Inverse Problems using Data and Machine Learning. - Erik Burman; Mats G. Larson; Karl Larsson 001; Carl Lundholm (CoRR, 2024)

Cut Finite Element Method for Divergence-Free Approximation of Incompressible Flow: A Lagrange Multiplier Approach. - Erik Burman; Peter Hansbo; Mats G. Larson (SIAM J. Numer. Anal., 2024)

WAN Discretization of PDEs: Best Approximation, Stabilization, and Essential Boundary Conditions. - Silvia Bertoluzza; Erik Burman; Cuiyu He (SIAM J. Sci. Comput., 2024)

Cut finite element methods. - Erik Burman; Peter Hansbo; Mats G. Larson; Sara Zahedi (Acta Numer., 2025)

Hybridized Augmented Lagrangian Methods for Contact Problems. - Erik Burman; Peter Hansbo; Mats G. Larson (CoRR, 2025)

Dynamic Ritz Projection for Finite Element Methods in Fluid-Structure Interaction. - Erik Burman; Buyang Li; Rong Tang (CoRR, 2025)

Unfitted hybrid high-order methods stabilized by polynomial extension for elliptic interface problems. - Erik Burman; Alexandre Ern; Romain Mottier (CoRR, 2025)

Numerical Approximation and Analysis of the Inverse Robin Problem Using the Kohn-Vogelius Method. - Erik Burman; Siyu Cen; Bangti Jin; Zhi Zhou 002 (CoRR, 2025)

Posterior contraction rates of computational methods for Bayesian data assimilation. - Erik Burman; Mingfei Lu (CoRR, 2025)

Optimal Approximation of Unique Continuation. - Erik Burman; Mihai Nechita; Lauri Oksanen (Found. Comput. Math., 2025)

Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method. - Erik Burman; Rebecca Durst; Miguel A. Fernández; Johnny Guzmán; Sijing Liu (Numer. Algorithms, 2025)

Robin-Robin Loose Coupling for Incompressible Fluid-Structure Interaction: Non-Linear Setting and Nearly-Optimal Error Analysis. - Erik Burman; Rebecca Durst; Miguel A. Fernández; Johnny Guzmán; Oscar Ruz (J. Sci. Comput., 2025)