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Journal of Computational and Applied Mathematics 265 151 (2014)
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Generalised element load method for first- and second-order element solutions with element load effect

C.K. Iu
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Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H (div)

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The Optimal Convergence of theh‐pVersion of the Finite Element Method with Quasi‐Uniform Meshes

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Galerkin Method with Discontinuous Basis Functions on Staggered Grips a Priory Estimates for the Homogeneous Dirichlet Problem

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Error estimate of fully discrete discontinuous Galerkin approximation for the viscoelasticity type equation

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Joachim Gwinner and Ernst Peter Stephan
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Explicit polynomial preserving trace liftings on a triangle

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The Numerical Methods for Oscillating Singularities in Elliptic Boundary Value Problems

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A discontinuoushp finite element method for the Euler and Navier-Stokes equations

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Benchmark computation and performance evaluation for a rhombic plate bending problem

Ivo Babuška and Terenzio Scapolla
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Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

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Journal of Scientific Computing 37 (2) 139 (2008)
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The p-version of the finite element method for the elliptic boundary value problems with interfaces

Hae-Soo Oh and Ivo Babuška
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A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems

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DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC PROBLEMS WITH MIXED BOUNDARY CONDITION

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A priori error estimations of hp-finite element approximations for hierarchical models of plate- and shell-like structures

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COMPARISON OFH ANDP FINITE ELEMENT APPROXIMATIONS OF THE SHALLOW WATER EQUATIONS

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Boundary-hybrid finite elements and a posteriori error estimation

Joseph M. Maubach and Patrick J. Rabier
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Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces

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SIAM Journal on Numerical Analysis 39 (5) 1512 (2002)
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Numerical study of theHP version of mixed discontinuous finite element methods for reaction-diffusion problems: The 1D case

Hongsen Chen, Zhangxin Chen and Baoyan Li
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A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations

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IMA Journal of Numerical Analysis (2018)
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A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

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A posteriori discontinuous Galerkin error estimator for linear elasticity

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Clemens Pechstein
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A first-second order splitting method for a third-order partial differential equation

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A higher-order finite element scheme for incompressible lubrication calculations

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Norbert Heuer and Florian Leydecker
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J. Tinsley Oden and Carlos Erik Baumann
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Andrzej Karafiat
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Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations

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A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities

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A new posteriori error estimates for a discontinuous Galerkin method for a reaction–diffusion problem

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Thomas Apel and Jens M. Melenk
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A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems

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Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws

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Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media

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hp spectral element approximation for integral state constrained optimal control problems governed by harmonic equations

Yanping Chen, Xiuxiu Lin, Yunqing Huang and Qian Lin
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The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains

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The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities

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Clemens Pechstein
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William F. Mitchell and Marjorie A. McClain
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Ahkmortar spectral element method for thep-Laplacian equation

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A finite element method dealing the singular points with a cut-off function

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Less is often more: Applied inverse problems using hp-forward models

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Journal of Computational Physics 399 108949 (2019)
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$hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes

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Paola F. Antonietti, Alberto Ferroni, Ilario Mazzieri and Alfio Quarteroni
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Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

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The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces

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Nataliya Rossokhata
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SPEED: SPectral Elements in Elastodynamics with Discontinuous Galerkin: a non-conforming approach for 3D multi-scale problems

I. Mazzieri, M. Stupazzini, R. Guidotti and C. Smerzini
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A posteriori error estimates of hp spectral element methods for optimal control problems with L2-norm state constraint

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The ultraspherical spectral element method

Daniel Fortunato, Nicholas Hale and Alex Townsend
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Mixed finite element methods for two-body contact problems

Andreas Schröder, Heiko Kleemann and Heribert Blum
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A posteriori error of a discontinuous Galerkin scheme for compressible miscible displacement problems with molecular diffusion and dispersion

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Quality assessment of the a-posteriori error estimation in finite elements

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Dong Qu, Jing Yang and Yubo Yang
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A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems

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An hp-adaptive strategy in a Petrov-Galerkin method for convection-diffusion problems

R. C. Almeida and R. S. Silva
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Clemens Pechstein
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P. Gervasio, A. Quarteroni and F. Saleri
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The weighted Ritz-Galerkin method for elliptic boundary value problems on unbounded domains

Hae-Soo Oh, Bongsoo Jang and Yichung Jou
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An iterative substructuring method for thehp-version of the BEM on quasi-uniform triangular meshes

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A priori hp-estimates for discontinuous Galerkin approximations to linear hyperbolic integro-differential equations

Samir Karaa, Amiya K. Pani and Sangita Yadav
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hp-version interior penalty DGFEMs for the biharmonic equation

Endre Süli and Igor Mozolevski
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A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem

Jiming Yang, Yanping Chen and Yunqing Huang
Applied Mathematics and Computation 334 141 (2018)
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On the exponential convergence of theh-p version for boundary element Galerkin methods on polygons

I. Babuška, B. Q. Guo and E. P. Stephan
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Preconditioners for thep-version of the Galerkin method for a coupled finite element/boundary element system

Norbert Heuer and Ernst P. Stephan
Numerical Methods for Partial Differential Equations 14 (1) 47 (1998)
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The p- and hp-versions of the virtual element method for elliptic eigenvalue problems

O. Čertík, F. Gardini, G. Manzini, L. Mascotto and G. Vacca
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A note on the design of hp-adaptive finite element methods for elliptic partial differential equations

Paul Houston and Endre Süli
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A finite element method using singular functions for Poisson equations: Mixed boundary conditions

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A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

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A Comparison of hp -Adaptive Strategies for Elliptic Partial Differential Equations

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Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids

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Jacobi Polynomials, Weighted Sobolev Spaces and Approximation Results of Some Singularities

Serge Nicaise
Mathematische Nachrichten 213 (1) 117 (2000)
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hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems

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SIAM Journal on Scientific Computing 23 (4) 1226 (2001)
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A stable Petrov-Galerkin method for convection-dominated problems

Regina C. Almeida and Renato S. Silva
Computer Methods in Applied Mechanics and Engineering 140 (3-4) 291 (1997)
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Locking effects in the finite element approximation of elasticity problems

Ivo Babuška and Manil Suri
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A dynamic adaptation scheme for general 3-D hybrid meshes

Yannis Kallinderis and Christos Kavouklis
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Exponential convergence of the hp virtual element method in presence of corner singularities

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Three-dimensional mixed explicit-implicit generalized Galerkin spectral element methods for high-speed turbulent compressible flows

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Computer Methods in Applied Mechanics and Engineering 135 (3-4) 343 (1996)
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Discontinuous Galerkin methods for simulating bioreactive transport of viruses in porous media

Shuyu Sun and Mary F. Wheeler
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A Hierarchical Domain Decomposition Preconditioner forh-PFinite Element Approximation on Locally Refined Meshes

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An hp finite element adaptive scheme to solve the Laplace model for fluid–solid vibrations

M.G. Armentano, C. Padra, R. Rodríguez and M. Scheble
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Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

Tobias Leicht and Ralf Hartmann
Journal of Computational Physics 229 (19) 7344 (2010)
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n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method

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Computer Methods in Applied Mechanics and Engineering 198 (21-26) 1726 (2009)
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High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations

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Polynomial Liftings on a Tetrahedron and Applications to the h-p Version of the Finite Element Method in Three Dimensions

Rafael Muñoz-Sola
SIAM Journal on Numerical Analysis 34 (1) 282 (1997)
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Approximation results for spectral methods with domain decomposition

Christine Bernardi and Yvon Maday
Applied Numerical Mathematics 6 (1-2) 33 (1989)
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Polynomial extensions of compatible polynomial traces in three dimensions

Faker Ben Belgacem
Computer Methods in Applied Mechanics and Engineering 116 (1-4) 235 (1994)
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Piotr Krzyżanowski
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Nodal High-Order Methods on Unstructured Grids

J.S Hesthaven and T Warburton
Journal of Computational Physics 181 (1) 186 (2002)
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Adaptive hpq-finite element methods of hierarchical models for plate- and shell-like structures

J.Tinsley Oden and J.R. Cho
Computer Methods in Applied Mechanics and Engineering 136 (3-4) 317 (1996)
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New Development of the P and H-P Version Finite Element Method with Quasi-Uniform Meshes for Elliptic Problems

Jian Ming Zhang and Yong He
Applied Mechanics and Materials 444-445 671 (2013)
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$C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints

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An $$hp$$ h p finite element adaptive scheme to solve the Poisson problem on curved domains

M. G. Armentano, C. Padra and M. Scheble
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ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS

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hp-Version discontinuous Galerkin methods for hyperbolic conservation laws

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A systematic strategy for simultaneous adaptive hp finite element mesh modification using nonlinear programming

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Discontinuous Galerkin Discretization and $hp$-Refinement for the Resolution of the Neutron Transport Equation

D. Fournier, R. Herbin and R. Le Tellier
SIAM Journal on Scientific Computing 35 (2) A936 (2013)
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Theh-p version of the finite element method for problems with interfaces

Benqi Guo and Hae-Soo Oh
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Fully Discrete Analysis of a Discontinuous Finite Element Method for the Keller-Segel Chemotaxis Model

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Eric Boillat
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Finite element solutions for three-dimensional elliptic boundary value problems on unbounded domains

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Stable and Compatible Polynomial Extensions in Three Dimensions and Applications to thepandh-pFinite Element Method

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SIAM Journal on Numerical Analysis 47 (2) 1195 (2009)
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A Locally Conservative Finite Element Method Based on Piecewise Constant Enrichment of the Continuous Galerkin Method

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SIAM Journal on Scientific Computing 31 (4) 2528 (2009)
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An unconditionally stable space–time FE method for the Korteweg–de Vries equation

Eirik Valseth and Clint Dawson
Computer Methods in Applied Mechanics and Engineering 371 113297 (2020)
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HIGHER ORDER DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

Mi Ray Ohm, Hyun Young Lee and Jun Yong Shin
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DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS

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Mathematical Models and Methods in Applied Sciences 12 (05) 689 (2002)
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On hp- error estimation in the BEM for a three-dimensional Helmholtz exterior problem

Andrzej Karafiat
Computer Methods in Applied Mechanics and Engineering 150 (1-4) 199 (1997)
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A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems

Shuyu Sun and Mary F. Wheeler
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A study on directional resistivity logging-while-drilling based on self-adaptive hp-FEM

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Clemens Pechstein
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Uniqueness of numerical solutions to nonlinear parabolic equations by a fully implicit discontinuous Galerkin method

Lunji Song and Jinhu Ma
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Stabilized spectral element approximation for the Navier-Stokes equations

P. Gervasio and F. Saleri
Numerical Methods for Partial Differential Equations 14 (1) 115 (1998)
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A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes

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SIAM Journal on Numerical Analysis 33 (4) 1358 (1996)
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The Convergence of the H-P Version of the Finite Element Method with Quasi-Uniform Meshes for Three Dimensional Poisson Problems with Edge Singularity

Jian Ming Zhang and Yong He
Applied Mechanics and Materials 644-650 1551 (2014)
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Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis and Paul Houston
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The p- and h-p versions of the finite element method, an overview

Ivo Babuška and Manil Suri
Computer Methods in Applied Mechanics and Engineering 80 (1-3) 5 (1990)
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Finite element analysis of a holonomic elastic-plastic problem

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Numerische Mathematik 60 (1) 493 (1991)
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New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model

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SIAM Journal on Numerical Analysis 47 (1) 386 (2009)
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Analysis of a Nonsymmetric Discontinuous Galerkin Method for Elliptic Problems: Stability and Energy Error Estimates

Mats G. Larson and A. Jonas Niklasson
SIAM Journal on Numerical Analysis 42 (1) 252 (2004)
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An explicit second order spectral element method for acoustic waves

Elena Zampieri and Luca F. Pavarino
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A spectral collocation method for eigenvalue problems of compact integral operators

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The Optimalp-Version Approximation of Singularities on Polyhedra in the Boundary Element Method

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SIAM Journal on Numerical Analysis 33 (2) 729 (1996)
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Asymptotics of the generalized Gegenbauer functions of fractional degree

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Journal of Approximation Theory 253 105378 (2020)
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