An h-r-Adaptive Approximate Riemann Solver for the Euler Equations in Two Dimensions. - Michael G. Edwards; J. Tinsley Oden; Leszek F. Demkowicz (SIAM J. Sci. Comput., 1993)

Discrete compactness and the approximation of Maxwell's equations in R3. - Peter Monk 001; Leszek F. Demkowicz (Math. Comput., 2001)

Analysis of a coupled finite-infinite element method for exterior Helmholtz problems. - Leszek F. Demkowicz; Frank Ihlenburg (Numerische Mathematik, 2001)

A Fully Automatic hp-Adaptivity. - Leszek F. Demkowicz; Waldemar Rachowicz; Ph. Devloo (J. Sci. Comput., 2002)

A Computational Infrastructure for Reliable Computer Simulations. - J. Tinsley Oden; James C. Browne; Ivo Babuska; Kenneth M. Liechti; Leszek F. Demkowicz (International Conference on Computational Science, 2003)

Full-wave analysis of dielectric waveguides at a given frequency. - L. Vardapetyan; Leszek F. Demkowicz (Math. Comput., 2003)

p Interpolation Error Estimates for Edge Finite Elements of Variable Order in Two Dimensions. - Leszek F. Demkowicz; Ivo Babuska (SIAM J. Numer. Anal., 2003)

A Dynamic Data Driven Computational Infrastructure for Reliable Computer Simulations. - J. Tinsley Oden; James C. Browne; Ivo Babuska; Chandrajit L. Bajaj; Leszek F. Demkowicz; L. Gray; Jon Bass; Yusheng Feng; Serge Prudhomme; Fabio Nobile; Raúl Tempone (International Conference on Computational Science, 2004)

Reconstruction of G 1 Surfaces With Biquartic Patches for HP Fe Simulations. - Dong Xue; Leszek F. Demkowicz; Chandrajit L. Bajaj (IMR, 2004)

Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations. - Jayadeep Gopalakrishnan; Joseph E. Pasciak; Leszek F. Demkowicz (SIAM J. Numer. Anal., 2004)

Development of a Computational Paradigm for Laser Treatment of Cancer. - J. Tinsley Oden; Kenneth R. Diller; Chandrajit L. Bajaj; James C. Browne; John D. Hazle; Ivo Babuska; Jon Bass; Leszek F. Demkowicz; Yusheng Feng; David Fuentes 001; Serge Prudhomme; Marissa Nichole Rylander; et al. (International Conference on Computational Science (3), 2006)

Parallel hp-Finite Element Simulations of 3D Resistivity Logging Instruments. - Maciej Paszynski; David Pardo; Leszek F. Demkowicz; Carlos Torres-Verdín (CE, 2006)

Two-Dimensional High-Accuracy Simulation of Resistivity Logging-While-Drilling (LWD) Measurements Using a Self-Adaptive Goal-Oriented hp Finite Element Method. - David Pardo; Leszek F. Demkowicz; Carlos Torres-Verdín; Maciej Paszynski (SIAM J. Appl. Math., 2006)

Discrete Compactness for the hp Version of Rectangular Edge Finite Elements. - Daniele Boffi; Martin Costabel; Monique Dauge; Leszek F. Demkowicz (SIAM J. Numer. Anal., 2006)

Simulation of multifrequency borehole resistivity measurements through metal casing using a goal-oriented hp finite-element method. - David Pardo; Carlos Torres-Verdín; Leszek F. Demkowicz (IEEE Trans. Geosci. Remote. Sens., 2006)

Using Cyber-Infrastructure for Dynamic Data Driven Laser Treatment of Cancer. - Chandrajit L. Bajaj; J. Tinsley Oden; Kenneth R. Diller; James C. Browne; John D. Hazle; Ivo Babuska; Jon Bass; L. Bidaut; Leszek F. Demkowicz; Andrew Elliott; Yusheng Feng; David Fuentes 001; et al. (International Conference on Computational Science (1), 2007)

Parallel, fully automatic hp-adaptive 3D finite element package. - Maciej Paszynski; Leszek F. Demkowicz (Eng. Comput., 2007)

A 3-D hp Finite/Infinite Element Method to Calculate Power Deposition in the Human Head. - Dong Xue; Leszek F. Demkowicz; Ling Hao (IEEE Trans. Biomed. Eng., 2007)

Polynomial extension operators for H1, H(curl) and H(div)-spaces on a cube. - Martin Costabel; Monique Dauge; Leszek F. Demkowicz (Math. Comput., 2008)

Polynomial Extension Operators. Part I. - Leszek F. Demkowicz; Jayadeep Gopalakrishnan; Joachim Schöberl (SIAM J. Numer. Anal., 2008)

PML Enhanced with a Self-Adaptive Goal-Oriented hp-Finite Element Method: Simulation of Through-Casing Borehole Resistivity Measurements. - David Pardo; Leszek F. Demkowicz; Carlos Torres-Verdín; C. Michler (SIAM J. Sci. Comput., 2008)

Polynomial Extension Operators. Part II. - Leszek F. Demkowicz; Jayadeep Gopalakrishnan; Joachim Schöberl (SIAM J. Numer. Anal., 2009)

A parallel direct solver for the self-adaptive hp Finite Element Method. - Maciej Paszynski; David Pardo; Carlos Torres-Verdín; Leszek F. Demkowicz; Victor M. Calo (J. Parallel Distributed Comput., 2010)

Mixed variable order h-finite element method for linear elasticity with weakly imposed symmetry. Curvilinear elements in 2D. - Weifeng Qiu; Leszek F. Demkowicz (Comput. Methods Appl. Math., 2011)

A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D. - J. Zitelli; Ignacio Muga; Leszek F. Demkowicz; Jayadeep Gopalakrishnan; David Pardo; Victor M. Calo (J. Comput. Phys., 2011)

Out-of-core multi-frontal solver for multi-physics hp adaptive problems. - Maciej Paszynski; David Pardo; Anna Paszynska; Leszek F. Demkowicz (ICCS, 2011)

Discrete Compactness for the p-Version of Discrete Differential Forms. - Daniele Boffi; Martin Costabel; Monique Dauge; Leszek F. Demkowicz; Ralf Hiptmair (SIAM J. Numer. Anal., 2011)

Analysis of the DPG Method for the Poisson Equation. - Leszek F. Demkowicz; Jayadeep Gopalakrishnan (SIAM J. Numer. Anal., 2011)

Mixed hp-Finite Element Method for Linear Elasticity with Weakly Imposed Symmetry: Stability Analysis. - Weifeng Qiu; Leszek F. Demkowicz (SIAM J. Numer. Anal., 2011)

Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version. - Antti H. Niemi; Ivo Babuska; Juhani Pitkäranta; Leszek F. Demkowicz (Eng. Comput., 2012)

Polynomial extension operators. Part III. - Leszek F. Demkowicz; Jayadeep Gopalakrishnan; Joachim Schöberl (Math. Comput., 2012)

A locking-free hp DPG method for linear elasticity with symmetric stresses. - Jamie Bramwell; Leszek F. Demkowicz; Jay Gopalakrishnan; Weifeng Qiu (Numerische Mathematik, 2012)

A primal DPG method without a first-order reformulation. - Leszek F. Demkowicz; Jayadeep Gopalakrishnan (Comput. Math. Appl., 2013)

Constructively well-posed approximation methods with unity inf-sup and continuity constants for partial differential equations. - Tan Bui-Thanh; Leszek F. Demkowicz; Omar Ghattas (Math. Comput., 2013)

A Unified Discontinuous Petrov-Galerkin Method and Its Analysis for Friedrichs' Systems. - Tan Bui-Thanh; Leszek F. Demkowicz; Omar Ghattas (SIAM J. Numer. Anal., 2013)

Robust DPG Method for Convection-Dominated Diffusion Problems. - Leszek F. Demkowicz; Norbert Heuer (SIAM J. Numer. Anal., 2013)

Minimum Residual and Least Squares Finite Element Methods. - Pavel B. Bochev; Leszek F. Demkowicz; Jay Gopalakrishnan; Max D. Gunzburger (Comput. Math. Appl., 2014)

A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms. - Jesse Chan; Norbert Heuer; Tan Bui-Thanh; Leszek F. Demkowicz (Comput. Math. Appl., 2014)

Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems. - Truman Ellis; Leszek F. Demkowicz; Jesse Chan (Comput. Math. Appl., 2014)

The DPG method for the Stokes problem. - Nathan V. Roberts; Tan Bui-Thanh; Leszek F. Demkowicz (Comput. Math. Appl., 2014)

A Posteriori Error Control for DPG Methods. - Carsten Carstensen; Leszek F. Demkowicz; Jayadeep Gopalakrishnan (SIAM J. Numer. Anal., 2014)

Orientation embedded high order shape functions for the exact sequence elements of all shapes. - Federico Fuentes; Brendan Keith; Leszek F. Demkowicz; Sriram Nagaraj (Comput. Math. Appl., 2015)

A discontinuous Petrov-Galerkin methodology for adaptive solutions to the incompressible Navier-Stokes equations. - Nathan V. Roberts; Leszek F. Demkowicz; Robert D. Moser (J. Comput. Phys., 2015)

Quasi-linear computational cost adaptive solvers for three dimensional modeling of heating of a human head induced by cell phone. - Robert Schaefer; Marcin Los; Marcin Sieniek; Leszek F. Demkowicz; Maciej Paszynski (J. Comput. Sci., 2015)

Breaking spaces and forms for the DPG method and applications including Maxwell equations. - Carsten Carstensen; Leszek F. Demkowicz; Jay Gopalakrishnan (Comput. Math. Appl., 2016)

Prof. Ivo Babuška. - Leszek F. Demkowicz; Rick Falk; Benqi Guo; Michael Vogelius; Zhimin Zhang (Comput. Math. Appl., 2017)

Minimum Residual and Least Squares Finite Element Methods II. - Marc I. Gerritsma; Carsten Carstensen; Leszek F. Demkowicz; Jay Gopalakrishnan (Comput. Math. Appl., 2017)

Construction of DPG Fortin operators for second order problems. - Sriram Nagaraj; Socratis Petrides; Leszek F. Demkowicz (Comput. Math. Appl., 2017)

An adaptive DPG method for high frequency time-harmonic wave propagation problems. - Socratis Petrides; Leszek F. Demkowicz (Comput. Math. Appl., 2017)

Goal-oriented adaptive mesh refinement for non-symmetric functional settings. - Brendan Keith; Ali Vaziri Astaneh; Leszek F. Demkowicz (CoRR, 2017)

Coupled variational formulations of linear elasticity and the DPG methodology. - Federico Fuentes; Brendan Keith; Leszek F. Demkowicz; Patrick Le Tallec (J. Comput. Phys., 2017)

A Spacetime DPG Method for the Schrödinger Equation. - Leszek F. Demkowicz; Jayadeep Gopalakrishnan; Sriram Nagaraj; Paulina Sepúlveda (SIAM J. Numer. Anal., 2017)

Recent Advances in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Methods. - Fleurianne Bertrand; Leszek F. Demkowicz; Jay Gopalakrishnan; Norbert Heuer (Comput. Methods Appl. Math., 2019)

Fast Integration of DPG Matrices Based on Sum Factorization for all the Energy Spaces. - Jaime Mora; Leszek F. Demkowicz (Comput. Methods Appl. Math., 2019)

Alternative Enriched Test Spaces in the DPG Method for Singular Perturbation Problems. - Jacob Salazar; Jaime Mora; Leszek F. Demkowicz (Comput. Methods Appl. Math., 2019)

A DPG Maxwell approach for studying nonlinear thermal effects in active gain fiber amplifiers. - Stefan Henneking; Jacob Grosek; Leszek F. Demkowicz (CoRR, 2019)

A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers. - Sriram Nagaraj; Jacob Grosek; Socratis Petrides; Leszek F. Demkowicz; Jaime Mora (J. Comput. Phys. X, 2019)

Goal-Oriented Adaptive Mesh Refinement for Discontinuous Petrov-Galerkin Methods. - Brendan Keith; Ali Vaziri Astaneh; Leszek F. Demkowicz (SIAM J. Numer. Anal., 2019)

The DPG-star method. - Leszek F. Demkowicz; Jay Gopalakrishnan; Brendan Keith (Comput. Math. Appl., 2020)

Construction of DPG Fortin operators revisited. - Leszek F. Demkowicz; Pietro Zanotti (Comput. Math. Appl., 2020)

Deep Learning Driven Self-adaptive Hp Finite Element Method. - Maciej Paszynski; Rafal Wojciech Grzeszczuk; David Pardo; Leszek F. Demkowicz (ICCS (1), 2021)

Analysis of non-conforming DPG methods on polyhedral meshes using fractional Sobolev norms. - Constantin Bacuta; Leszek F. Demkowicz; Jaime Mora; Christos Xenophontos (Comput. Math. Appl., 2021)

Recent Advances in Least-Squares and Discontinuous Petrov-Galerkin Finite Element Methods. - Fleurianne Bertrand; Leszek F. Demkowicz; Jay Gopalakrishnan (Comput. Math. Appl., 2021)

The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi). - Leszek F. Demkowicz; Thomas Führer; Norbert Heuer; Xiaochuan Tian (Comput. Math. Appl., 2021)

A numerical study of the pollution error and DPG adaptivity for long waveguide simulations. - Stefan Henneking; Leszek F. Demkowicz (Comput. Math. Appl., 2021)

Model and computational advancements to full vectorial Maxwell model for studying fiber amplifiers. - Stefan Henneking; Jacob Grosek; Leszek F. Demkowicz (Comput. Math. Appl., 2021)

An Lp-DPG method for the convection-diffusion problem. - Jiaqi Li; Leszek F. Demkowicz (Comput. Math. Appl., 2021)

An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics. - Socratis Petrides; Leszek F. Demkowicz (Comput. Math. Appl., 2021)

Stabilized finite element methods for a fully-implicit logarithmic reformulation of the Oldroyd-B constitutive law. - Stefan Wittschieber; Leszek F. Demkowicz; Marek Behr (CoRR, 2021)

Equivalence between the DPG method and the exponential integrators for linear parabolic problems. - Judit Muñoz-Matute; David Pardo; Leszek F. Demkowicz (J. Comput. Phys., 2021)

Deep Neural Networks and Smooth Approximation of PDEs. - Kamil Doleglo; Maciej Paszynski; Leszek F. Demkowicz (ICCS (1), 2022)

An L𝓅-DPG Method with Application to 2D Convection-Diffusion Problems. - Jiaqi Li; Leszek F. Demkowicz (Comput. Methods Appl. Math., 2022)

Deep neural networks for smooth approximation of physics with higher order and continuity B-spline base functions. - Kamil Doleglo; Anna Paszynska; Maciej Paszynski; Leszek F. Demkowicz (CoRR, 2022)

hp3D User Manual. - Stefan Henneking; Leszek F. Demkowicz (CoRR, 2022)

A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. - Yu Leng; Xiaochuan Tian; Leszek F. Demkowicz; Héctor Gómez; John T. Foster (J. Comput. Phys., 2022)

The DPG Method for the Convection-Reaction Problem, Revisited. - Leszek F. Demkowicz; Nathan V. Roberts; Judit Muñoz-Matute (Comput. Methods Appl. Math., 2023)

Multistage DPG time-marching scheme for nonlinear problems. - Judit Muñoz-Matute; Leszek F. Demkowicz (CoRR, 2023)

Scalable DPG multigrid solver for Helmholtz problems: A study on convergence. - Jacob C. Badger; Stefan Henneking; Socratis Petrides; Leszek F. Demkowicz (Comput. Math. Appl., 2023)

An anisotropic hp-adaptation framework for ultraweak discontinuous Petrov-Galerkin formulations. - Ankit Chakraborty; Stefan Henneking; Leszek F. Demkowicz (Comput. Math. Appl., 2024)

A DPG method for planar div-curl problems. - Jiaqi Li; Leszek F. Demkowicz (Comput. Math. Appl., 2024)

A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schrödinger Equation for Laser Pulse Propagation in Waveguides. - Ankit Chakraborty; Judit Muñoz-Matute; Leszek F. Demkowicz; Jacob Grosek (CoRR, 2024)

Multistage Discontinuous Petrov-Galerkin Time-Marching Scheme for Nonlinear Problems. - Judit Muñoz-Matute; Leszek F. Demkowicz (SIAM J. Numer. Anal., 2024)

$hp mathrm{3D}$: A Scalable MPI/OpenMP $hp$-Adaptive Finite Element Software Library for Complex Multiphysics Applications. - Stefan Henneking; Socratis Petrides; Federico Fuentes; Jacob C. Badger; Leszek F. Demkowicz (J. Open Source Softw., 2024)

Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides. - Leszek F. Demkowicz; Jens Markus Melenk; Jacob C. Badger; Stefan Henneking (Adv. Comput. Math., 2024)

The discontinuous Petrov-Galerkin method. - Leszek F. Demkowicz; Jay Gopalakrishnan (Acta Numer., 2025)

A vectorial envelope Maxwell formulation for electromagnetic waveguides with application to nonlinear fiber optics. - Stefan Henneking; Jacob Grosek; Leszek F. Demkowicz (Comput. Math. Appl., 2025)

Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides. - Jens Markus Melenk; Leszek F. Demkowicz; Stefan Henneking (SIAM J. Math. Anal., 2025)