Spectral convergence for orthogonal polynomials on triangles. - Philipp Öffner; Thomas Sonar (Numerische Mathematik, 2013)

Summation-by-parts operators for correction procedure via reconstruction. - Hendrik Ranocha; Philipp Öffner; Thomas Sonar (J. Comput. Phys., 2016)

Extended skew-symmetric form for summation-by-parts operators and varying Jacobians. - Hendrik Ranocha; Philipp Öffner; Thomas Sonar (J. Comput. Phys., 2017)

L2 Stability of Explicit Runge-Kutta Schemes. - Hendrik Ranocha; Philipp Öffner (J. Sci. Comput., 2018)

Application of modal filtering to a spectral difference method. - Jan Glaubitz; Philipp Öffner; Thomas Sonar (Math. Comput., 2018)

A class of finite dimensional spaces and H(div) conformal elements on general polytopes. - Rémi Abgrall; Élise Le Mélédo; Philipp Öffner (CoRR, 2019)

Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes. - Rémi Abgrall; Philipp Öffner; Hendrik Ranocha (CoRR, 2019)

General polytopial H(div) conformal finite elements and their discretisation spaces. - Rémi Abgrall; Élise Le Mélédo; Philipp Öffner (CoRR, 2019)

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability. - Rémi Abgrall; Jan Nordström; Philipp Öffner; Svetlana V. Tokareva (CoRR, 2019)

Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients. - Philipp Öffner; Hendrik Ranocha (J. Sci. Comput., 2019)

Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points. - Jan Glaubitz; Philipp Öffner (CoRR, 2020)

DeC and ADER: Similarities, Differences and an Unified Framework. - Maria Han Veiga; Philipp Öffner; Davide Torlo (CoRR, 2020)

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems. - Rémi Abgrall; Jan Nordström; Philipp Öffner; Svetlana V. Tokareva (J. Sci. Comput., 2020)

Towards stable radial basis function methods for linear advection problems. - Jan Glaubitz; Élise Le Mélédo; Philipp Öffner (Comput. Math. Appl., 2021)

Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes. - Rémi Abgrall; Élise Le Mélédo; Philipp Öffner; Davide Torlo (CoRR, 2021)

A New Stability Approach for Positivity-Preserving Patankar-type Schemes. - Davide Torlo; Philipp Öffner; Hendrik Ranocha (CoRR, 2021)

An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations. - Mirco Ciallella; Lorenzo Micalizzi; Philipp Öffner; Davide Torlo (CoRR, 2021)

DeC and ADER: Similarities, Differences and a Unified Framework. - Maria Han Veiga; Philipp Öffner; Davide Torlo (J. Sci. Comput., 2021)

Comparison to control oscillations in high-order Finite Volume schemes via physical constraint limiters, neural networks and polynomial annihilation. - Dorian Hillebrand; Simon-Christian Klein; Philipp Öffner (CoRR, 2022)

High order entropy preserving ADER scheme. - Elena Gaburro; Philipp Öffner; Mario Ricchiuto; Davide Torlo (CoRR, 2022)

On the Stability of Modified Patankar Methods. - Thomas Izgin; Philipp Öffner (CoRR, 2022)

On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions. - Rémi Abgrall; Mária Lukácová-Medvid'ová; Philipp Öffner (CoRR, 2022)

Entropy conservative high-order fluxes in the presence of boundaries. - Simon-Christian Klein; Philipp Öffner (CoRR, 2022)

A necessary condition for non oscillatory and positivity preserving time-integration schemes. - Thomas Izgin; Philipp Öffner; Davide Torlo (CoRR, 2022)

Fully well balanced entropy controlled DGSEM for shallow water flows: global flux quadrature and cell entropy correction. - Yogiraj Mantri; Philipp Öffner; Mario Ricchiuto (CoRR, 2022)

Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: Application to structure preserving discretization. - Rémi Abgrall; Philipp Öffner; Hendrik Ranocha (J. Comput. Phys., 2022)

High order entropy preserving ADER-DG schemes. - Elena Gaburro; Philipp Öffner; Mario Ricchiuto; Davide Torlo (Appl. Math. Comput., 2023)

Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions. - Mária Lukácová-Medvid'ová; Philipp Öffner (Appl. Math. Comput., 2023)

A new variable shape parameter strategy for RBF approximation using neural networks. - Fatemeh Nassajian Mojarrad; Maria Han Veiga; Jan S. Hesthaven; Philipp Öffner (Comput. Math. Appl., 2023)

Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems. - Dmitri Kuzmin; Mária Lukácová-Medvid'ová; Philipp Öffner (CoRR, 2023)

High-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (CoRR, 2023)

Summation-by-Parts Operators for General Function Spaces. - Jan Glaubitz; Jan Nordström; Philipp Öffner (SIAM J. Numer. Anal., 2023)

Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction. - Jan Glaubitz; Simon-Christian Klein; Jan Nordström; Philipp Öffner (J. Comput. Phys., 2023)

Applications of Limiters, Neural Networks and Polynomial Annihilation in Higher-Order FD/FV Schemes. - Dorian Hillebrand; Simon-Christian Klein; Philipp Öffner (J. Sci. Comput., 2023)

A high-order, fully well-balanced, unconditionally positivity-preserving finite volume framework for flood simulations. - Mirco Ciallella; Lorenzo Micalizzi; Victor Michel-Dansac; Philipp Öffner; Davide Torlo (CoRR, 2024)

Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations. - Philipp Öffner; Louis Petri; Davide Torlo (CoRR, 2024)

An optimization-based construction procedure for function space based summation-by-parts operators on arbitrary grids. - Jan Glaubitz; Jan Nordström; Philipp Öffner (CoRR, 2024)

Locally energy-stable finite element schemes for incompressible flow problems: Design and analysis for equal-order interpolations. - Hennes Hajduk; Dmitri Kuzmin; Gert Lube; Philipp Öffner (CoRR, 2024)

Discontinuous Galerkin methods for the complete stochastic Euler equations. - Dominic Breit; Thamsanqa Castern Moyo; Philipp Öffner (CoRR, 2024)

Summation-by-parts operators for general function spaces: The second derivative. - Jan Glaubitz; Simon-Christian Klein; Jan Nordström; Philipp Öffner (J. Comput. Phys., 2024)

Energy-Stable Global Radial Basis Function Methods on Summation-By-Parts Form. - Jan Glaubitz; Jan Nordström; Philipp Öffner (J. Sci. Comput., 2024)

Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: Global flux quadrature and cell entropy correction. - Yogiraj Mantri; Philipp Öffner; Mario Ricchiuto (J. Comput. Phys., 2024)

Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. - Jan Glaubitz; Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Gregor Gassner (J. Comput. Phys., 2025)

On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (J. Comput. Phys., 2025)

The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws. - Janina Bender; Thomas Izgin; Philipp Öffner; Davide Torlo (CoRR, 2025)