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ORCIDSIAM Journal on Numerical Analysis, Volume 54
Volume 54, Number 1, 2016
- Pauline Lafitte
, Annelies Lejon, Giovanni Samaey:
A High-Order Asymptotic-Preserving Scheme for Kinetic Equations Using Projective Integration. 1-33 - Paola F. Antonietti, Lourenço Beirão da Veiga, Simone Scacchi, Marco Verani:
A C1 Virtual Element Method for the Cahn-Hilliard Equation with Polygonal Meshes. 34-56 - Jean-Luc Guermond, Bojan Popov:
Error Estimates of a First-order Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations. 57-85 - Andy T. S. Wan, Alexander Bihlo, Jean-Christophe Nave:
The Multiplier Method to Construct Conservative Finite Difference Schemes for Ordinary and Partial Differential Equations. 86-119 - Emmanuil H. Georgoulis, Omar Lakkis, Charalambos G. Makridakis, Juha M. Virtanen:
A Posteriori Error Estimates for Leap-Frog and Cosine Methods for Second Order Evolution Problems. 120-136 - Martin Campos Pinto, Frédérique Charles:
Uniform Convergence of a Linearly Transformed Particle Method for the Vlasov-Poisson System. 137-160 - Yves Achdou, Alessio Porretta:
Convergence of a Finite Difference Scheme to Weak Solutions of the System of Partial Differential Equations Arising in Mean Field Games. 161-186 - Florent Renac:
Stability Analysis of Discontinuous Galerkin Discrete Shock Profiles for Steady Scalar Conservation Laws. 187-209 - Beniamin Bogosel, Bozhidar Velichkov:
A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results. 210-241 - Stefano Berrone, Andrea Borio, Stefano Scialò:
A Posteriori Error Estimate for a PDE-Constrained Optimization Formulation for the Flow in DFNs. 242-261 - Volker Michel, Roger Telschow:
The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems. 262-287 - Thi-Thao-Phuong Hoang, Caroline Japhet, Michel Kern, Jean E. Roberts:
Space-Time Domain Decomposition for Reduced Fracture Models in Mixed Formulation. 288-316 - Francesca Tantardini, Andreas Veeser:
The L2-Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations. 317-340 - Claudia König, Frank Werner, Thorsten Hohage:
Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise. 341-360 - Andreas Potschka:
Backward Step Control for Global Newton-Type Methods. 361-387 - Jörg Grande, Arnold Reusken:
A Higher Order Finite Element Method for Partial Differential Equations on Surfaces. 388-414 - Muruhan Rathinam:
Convergence of Moments of tau Leaping Schemes for Unbounded Markov Processes on Integer Lattices. 415-439 - Kerstin Küpper, Martin Frank, Shi Jin:
An Asymptotic Preserving Two-dimensional Staggered Grid Method for Multiscale Transport Equations. 440-461 - Libin Jiao, Bo Dong, Jintao Zhang, Bo Yu:
Polynomial Homotopy Method for the Sparse Interpolation Problem Part I: Equally Spaced Sampling. 462-480 - Bangti Jin, Raytcho D. Lazarov, Zhi Zhou:
A Petrov-Galerkin Finite Element Method for Fractional Convection-Diffusion Equations. 481-503
Volume 54, Number 2, 2016
- David F. Anderson, Desmond J. Higham, Yu Sun:
Multilevel Monte Carlo for Stochastic Differential Equations with Small Noise. 505-529 - Qinghai Zhang, Aaron L. Fogelson:
MARS: An Analytic Framework of Interface Tracking via Mapping and Adjusting Regular Semialgebraic Sets. 530-560 - Dmitriy Leykekhman, Boris Vexler:
Finite Element Pointwise Results on Convex Polyhedral Domains. 561-587 - Giuseppe Maria Coclite, O. Reichmann, Nils Henrik Risebro:
A Convergent Difference Scheme for a Class of Partial Integro-Differential Equations Modeling Pricing under Uncertainty. 588-605 - Shanzhen Chen, Fawang Liu, X. Jiang, Ian W. Turner, Kevin Burrage:
Fast Finite Difference Approximation for Identifying Parameters in a Two-dimensional Space-fractional Nonlocal Model with Variable Diffusivity Coefficients. 606-624 - Wei Hong Yang, Deren Han:
Linear Convergence of the Alternating Direction Method of Multipliers for a Class of Convex Optimization Problems. 625-640 - Thomas Rey, Changhui Tan:
An Exact Rescaling Velocity Method for some Kinetic Flocking Models. 641-664 - Roy R. Lederman, Vladimir Rokhlin:
On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II. 665-687 - Roland Herzog, Susann Mach:
Preconditioned Solution of State Gradient Constrained Elliptic Optimal Control Problems. 688-718 - Vanni Noferini, Alex Townsend:
Numerical Instability of Resultant Methods for Multidimensional Rootfinding. 719-743 - Markus Bachmayr, Wolfgang Dahmen:
Adaptive Low-Rank Methods: Problems on Sobolev Spaces. 744-796 - Michael S. Floater, Ming-Jun Lai:
Polygonal Spline Spaces and the Numerical Solution of the Poisson Equation. 797-824 - Xiaobing Feng, Yukun Li, Yulong Xing:
Analysis of Mixed Interior Penalty Discontinuous Galerkin Methods for the Cahn-Hilliard Equation and the Hele-Shaw Flow. 825-847 - Ricardo H. Nochetto, Enrique Otárola, Abner J. Salgado:
A PDE Approach to Space-Time Fractional Parabolic Problems. 848-873 - Mohammad Zakerzadeh, Georg May:
On the Convergence of a Shock Capturing Discontinuous Galerkin Method for Nonlinear Hyperbolic Systems of Conservation Laws. 874-898 - Ran Zhang, Hui Liang, Hermann Brunner:
Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations. 899-920 - Marc Dambrine, Isabelle Greff, Helmut Harbrecht, Bénédicte Puig:
Numerical Solution of the Poisson Equation on Domains with a Thin Layer of Random Thickness. 921-941 - Jan Martin Nordbotten:
Stable Cell-Centered Finite Volume Discretization for Biot Equations. 942-968 - Mario Ullrich, Tino Ullrich:
The Role of Frolov's Cubature Formula for Functions with Bounded Mixed Derivative. 969-993 - T. Chacón Rebollo, Vivette Girault, François Murat, Olivier Pironneau:
Analysis of a Coupled Fluid-Structure Model with Applications to Hemodynamics. 994-1019 - Emil Kieri, Christian Lubich, Hanna Walach:
Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values. 1020-1038 - Marco Discacciati, Paola Gervasio, Alessandro Giacomini, Alfio Quarteroni:
The Interface Control Domain Decomposition Method for Stokes-Darcy Coupling. 1039-1068 - Jessika Camaño, Gabriel N. Gatica, Ricardo Oyarzúa, Giordano Tierra:
An Augmented Mixed Finite Element Method for the Navier-Stokes Equations with Variable Viscosity. 1069-1092 - Rikard Anton, David Cohen, Stig Larsson, Xiaojie Wang:
Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise. 1093-1119 - Francis Filbet, Luis Miguel Rodrigues:
Asymptotically Stable Particle-In-Cell Methods for the Vlasov-Poisson System with a Strong External Magnetic Field. 1120-1146 - Binjie Li, Xiaoping Xie:
BPX Preconditioner for Nonstandard Finite Element Methods for Diffusion Problems. 1147-1168 - René Schneider, Gerd Wachsmuth:
A Posteriori Error Estimation for Control-Constrained, Linear-Quadratic Optimal Control Problems. 1169-1192 - Huo-Yuan Duan, Ping Lin, Roger C. E. Tan:
A Finite Element Method for a Curlcurl-Graddiv Eigenvalue Interface Problem. 1193-1228 - Wei Gong, Ningning Yan:
Finite Element Approximations of Parabolic Optimal Control Problems with Controls Acting on a Lower Dimensional Manifold. 1229-1262 - Clément Cancès, Hélène Mathis, Nicolas Seguin:
Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws. 1263-1287 - Christopher Keim, Holger Wendland:
A High-Order, Analytically Divergence-Free Approximation Method for the Time-Dependent Stokes Problem. 1288-1312 - Praveen Chandrashekar, Christian Klingenberg:
Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes. 1313-1340
Volume 54, Number 3, 2016
- Parsiad Azimzadeh, Peter A. Forsyth:
Weakly Chained Matrices, Policy Iteration, and Impulse Control. 1341-1364 - Dmitriy Leykekhman, Boris Vexler:
Pointwise Best Approximation Results for Galerkin Finite Element Solutions of Parabolic Problems. 1365-1384 - Martin Halla:
Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems. 1385-1400 - Dang-Manh Nguyen, Jörg Peters:
Nonuniform Discontinuous Galerkin Filters via Shift and Scale. 1401-1422 - Michael Feischl, Dirk Praetorius, Kristoffer G. van der Zee:
An Abstract Analysis of Optimal Goal-Oriented Adaptivity. 1423-1448 - Christian Bayer, Peter K. Friz, Sebastian Riedel, John Schoenmakers:
From Rough Path Estimates to Multilevel Monte Carlo. 1449-1483 - Magnus Svärd:
A Convergent Numerical Scheme for the Compressible Navier-Stokes Equations. 1484-1506 - Assyr Abdulle, Timothée Pouchon:
A Priori Error Analysis of the Finite Element Heterogeneous Multiscale Method for the Wave Equation over Long Time. 1507-1534 - William W. Hager, Maryam Yashtini, Hongchao Zhang:
An O(1/k) Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm. 1535-1556 - Haiyong Wang:
On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients. 1557-1581 - Jean-Marie Mirebeau:
Minimal Stencils for Discretizations of Anisotropic PDEs Preserving Causality or the Maximum Principle. 1582-1611 - Weizhang Huang, Lennard Kamenski, Jens Lang:
Stability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes. 1612-1634 - Matthew F. Causley, Hana Cho, Andrew J. Christlieb, David C. Seal:
Method of Lines Transpose: High Order L-Stable O(N) Schemes for Parabolic Equations Using Successive Convolution. 1635-1652 - Dong Li, Zhonghua Qiao, Tao Tang:
Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations. 1653-1681 - François P. Hamon, Hamdi A. Tchelepi:
Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity. 1682-1712 - Yvon Maday, Olga Mula, Gabriel Turinici:
Convergence analysis of the Generalized Empirical Interpolation Method. 1713-1731 - John W. Barrett, Harald Garcke, Robert Nürnberg:
Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects. 1732-1762 - Kim Ngan Le, William McLean, Kassem Mustapha:
Numerical Solution of the Time-Fractional Fokker-Planck Equation with General Forcing. 1763-1784 - Weizhu Bao, Yongyong Cai, Xiaowei Jia, Qinglin Tang:
A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime. 1785-1812 - Håkon Hoel, Kody J. H. Law, Raúl Tempone:
Multilevel ensemble Kalman filtering. 1813-1839 - Konstantinos Dareiotis, Chaman Kumar, Sotirios Sabanis:
On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations. 1840-1872 - Florent Chave, Daniele A. Di Pietro, Fabien Marche, Franck Pigeonneau:
A Hybrid High-Order Method for the Cahn-Hilliard problem in Mixed Form. 1873-1898 - Qiang Du, Jiang Yang:
Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen-Cahn Equations. 1899-1919 - Ulrik S. Fjordholm, Susanne Solem:
Second-Order Convergence of Monotone Schemes for Conservation Laws. 1920-1945 - Kinjal Basu, Art B. Owen:
Transformations and Hardy-Krause Variation. 1946-1966 - Erik Burman, Friedhelm Schieweck:
Local CIP Stabilization for Composite Finite Elements. 1967-1992 - Yuto Miyatake, John C. Butcher:
A Characterization of Energy-Preserving Methods and the Construction of Parallel Integrators for Hamiltonian Systems. 1993-2013
Volume 54, Number 4, 2016
- Zhi Zhao, Xiao-Qing Jin, Zheng-Jian Bai:
A Geometric Nonlinear Conjugate Gradient Method for Stochastic Inverse Eigenvalue Problems. 2015-2035 - Yu-Wen Li, Xinyuan Wu:
Functionally Fitted Energy-Preserving Methods for Solving Oscillatory Nonlinear Hamiltonian Systems. 2036-2059 - Jin Zhang, Xiaowei Liu, Min Yang:
Optimal Order L2 Error Estimate of SDFEM on Shishkin Triangular Meshes for Singularly Perturbed Convection-Diffusion Equations. 2060-2080 - Shuhuang Xiang:
On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity. 2081-2113 - Yuling Jiao, Qinian Jin, Xiliang Lu, Weijie Wang:
Alternating Direction Method of Multipliers for Linear Inverse Problems. 2114-2137 - Mira Schedensack:
A New Discretization for mth-Laplace Equations with Arbitrary Polynomial Degrees. 2138-2162 - Philipp Morgenstern:
Globally Structured Three-Dimensional Analysis-Suitable T-Splines: Definition, Linear Independence and m-graded local refinement. 2163-2186 - Benjamin Gess, Benoît Perthame, Panagiotis E. Souganidis:
Semi-discretization for Stochastic Scalar Conservation Laws with Multiple Rough Fluxes. 2187-2209 - Iván Area, Dimitar K. Dimitrov, Eduardo Godoy, Vanessa G. Paschoa:
Approximate Calculation of Sums II: Gaussian Type Quadrature. 2210-2227 - Christoph Erath, Dirk Praetorius:
Adaptive Vertex-Centered Finite Volume Methods with Convergence Rates. 2228-2255 - Ben Adcock, Rodrigo B. Platte:
A Mapped Polynomial Method for High-Accuracy Approximations on Arbitrary Grids. 2256-2281 - Guohui Song, Jacqueline Davis, Anne Gelb:
A High-Dimensional Inverse Frame Operator Approximation Technique. 2282-2301 - Wen-ming He, Runchang Lin, Zhimin Zhang:
Ultraconvergence of Finite Element Method by Richardson Extrapolation for Elliptic Problems with Constant Coefficients. 2302-2322 - Eberhard Bänsch, Andreas Brenner:
A Posteriori Error Estimates for Pressure-Correction Schemes. 2323-2358 - Fabian Brunner, Julian Fischer, Peter Knabner:
Analysis of a Modified Second-Order Mixed Hybrid BDM1 Finite Element Method for Transport Problems in Divergence Form. 2359-2378 - Andrea Bonito, Alan Demlow:
Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters. 2379-2388 - Sebastian Becker, Arnulf Jentzen, Peter E. Kloeden:
An Exponential Wagner-Platen Type Scheme for SPDEs. 2389-2426 - Gabriel R. Barrenechea, Volker John, Petr Knobloch:
Analysis of Algebraic Flux Correction Schemes. 2427-2451 - Georg May, Mohammad Zakerzadeh:
On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws. 2452-2465 - Jean-Luc Guermond, Bojan Popov:
Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems. 2466-2489 - Marc J. Piggott, Victor Solo:
Geometric Euler-Maruyama Schemes for Stochastic Differential Equations in SO(n) and SE(n). 2490-2516 - Mark S. Gockenbach:
Generalizing the GSVD. 2517-2540 - Josef Dick, Frances Y. Kuo, Quoc Thong Le Gia, Christoph Schwab:
Multilevel Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations. 2541-2568 - Chuchu Chen, Jialin Hong:
Symplectic Runge-Kutta Semidiscretization for Stochastic Schrödinger Equation. 2569-2593 - Barbara Kaltenbacher:
Regularization Based on All-At-Once Formulations for Inverse Problems. 2594-2618 - Enrique Otárola, Abner J. Salgado:
Finite Element Approximation of the Parabolic Fractional Obstacle Problem. 2619-2639 - Hui Liang, Hermann Brunner:
Integral-Algebraic Equations: Theory of Collocation Methods II. 2640-2663 - Takashi Goda, Kosuke Suzuki, Takehito Yoshiki:
An Explicit Construction of Optimal Order Quasi-Monte Carlo Rules for Smooth Integrands. 2664-2683 - Roland Becker, Daniela Capatina, Robert Luce:
Local Flux Reconstructions for Standard Finite Element Methods on Triangular Meshes. 2684-2706 - Christoph Pflaum, Rainer Hartmann:
A Sparse Grid Discretization of the Helmholtz Equation with Variable Coefficients in High Dimensions. 2707-2727
Volume 54, Number 5, 2016
- Xiang Wang, Yonghai Li:
L2 Error Estimates for High Order Finite Volume Methods on Triangular Meshes. 2729-2749 - Qingguo Hong, Johannes Kraus:
Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem. 2750-2774 - Sofia Lindqvist, Peder Aursand, Tore Flåtten, Anders Aase Solberg:
Large Time Step TVD Schemes for Hyperbolic Conservation Laws. 2775-2798 - Yiannis Hadjimichael, David I. Ketcheson, Lajos Lóczi, Adrián Németh:
Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size. 2799-2832 - Yuhong Zhang, Yanren Hou, Li Shan:
Stability and Convergence Analysis of a Decoupled Algorithm for a Fluid-Fluid Interaction Problem. 2833-2867 - Cesáreo González, Mechthild Thalhammer:
Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part II: Convergence. 2868-2888 - Manas Rachh, Leslie Greengard:
Integral Equation Methods for Elastance and Mobility Problems in Two Dimensions. 2889-2909 - Kartikey Asthana, Jerry Watkins, Antony Jameson:
On the Rate of Convergence of Flux Reconstruction for Steady-State Problems. 2910-2937 - Weiping Shen, Chong Li, Jen-Chih Yao:
Convergence Analysis of Newton-Like Methods for Inverse Eigenvalue Problems with Multiple Eigenvalues. 2938-2950 - Ricardo Oyarzúa, Ricardo Ruiz-Baier:
Locking-Free Finite Element Methods for Poroelasticity. 2951-2973 - Jehanzeb Hameed Chaudhry, Donald J. Estep, Simon Tavener, Varis Carey, Jeff Sandelin:
A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm. 2974-3002 - Caroline Moosmüller:
C1 Analysis of Hermite Subdivision Schemes on Manifolds. 3003-3031 - Martina Bukac, Boris Muha:
Stability and Convergence Analysis of the Extensions of the Kinematically Coupled Scheme for the Fluid-Structure Interaction. 3032-3061 - Eduard Feireisl, Radim Hosek, Martin Michálek:
A Convergent Numerical Method for the Full Navier-Stokes-Fourier System in Smooth Physical Domains. 3062-3082 - Martin Parisot, Jean-Paul Vila:
Centered-Potential Regularization for the Advection Upstream Splitting Method. 3083-3104 - Todd Arbogast, Abraham L. Taicher:
A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures. 3105-3122 - Kelong Cheng, Cheng Wang:
Long Time Stability of High Order MultiStep Numerical Schemes for Two-Dimensional Incompressible Navier-Stokes Equations. 3123-3144 - Lulu Liu, David E. Keyes:
Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm. 3145-3166 - Marlis Hochbruck, Andreas Sturm:
Error Analysis of a Second-Order Locally Implicit Method for Linear Maxwell's Equations. 3167-3191
Volume 54, Number 6, 2016
- Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson, Marco Verani:
Adaptive Spectral Galerkin Methods with Dynamic Marking. 3193-3213 - M. Paul Laiu, Cory D. Hauck, Ryan G. McClarren, Dianne P. O'Leary, André L. Tits:
Positive Filtered PN Moment Closures for Linear Kinetic Equations. 3214-3238 - Alfonso Álamo, Jesús María Sanz-Serna:
A Technique for Studying Strong and Weak Local Errors of Splitting Stochastic Integrators. 3239-3257 - Paul C. Leopardi, Ari Stern:
The Abstract Hodge-Dirac Operator and Its Stable Discretization. 3258-3279 - Stevan Bellec, Mathieu Colin, Mario Ricchiuto:
Discrete Asymptotic Equations for Long Wave Propagation. 3280-3299 - Wanting Xu, Mihai Anitescu:
A Limited-Memory Multiple Shooting Method for Weakly Constrained Variational Data Assimilation. 3300-3331 - Todd Arbogast, Maicon R. Correa:
Two Families of H(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension. 3332-3356 - Can Huang, Yujian Jiao, Li-Lian Wang, Zhimin Zhang:
Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions. 3357-3387 - Carsten Carstensen, Friederike Hellwig:
Low-Order Discontinuous Petrov-Galerkin Finite Element Methods for Linear Elasticity. 3388-3410 - Andrea Cangiani, Vitaliy Gyrya, Gianmarco Manzini:
The NonConforming Virtual Element Method for the Stokes Equations. 3411-3435 - Santiago Badia, Hieu Nguyen:
Balancing Domain Decomposition by Constraints and Perturbation. 3436-3464 - Quentin Mérigot, Jean-Marie Mirebeau:
Minimal Geodesics Along Volume-Preserving Maps, Through Semidiscrete Optimal Transport. 3465-3492 - Patrick Henning, Mario Ohlberger, Barbara Verfürth:
A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations. 3493-3522 - Andreas Dedner, Jan Giesselmann:
A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws. 3523-3549 - Johanna Ridder:
Convergence of a Finite Difference Scheme for Two-Dimensional Incompressible Magnetohydrodynamics. 3550-3576 - Herbert Egger, Matthias Schlottbom:
A class of Galerkin Schemes for Time-Dependent Radiative Transfer. 3577-3599 - Balázs Kovács, Buyang Li, Christian Lubich:
A-Stable Time Discretizations Preserve Maximal Parabolic Regularity. 3600-3624 - Thomas Kühn, Sebastian Mayer, Tino Ullrich:
Counting Via Entropy: New Preasymptotics for the Approximation Numbers of Sobolev Embeddings. 3625-3647 - Fleurianne Bertrand, Gerhard Starke:
Parametric Raviart-Thomas Elements for Mixed Methods on Domains with Curved Surfaces. 3648-3667
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