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- Ainsworth, Mark, Davydov, Oleg, Schumaker, Larry L. Bernstein-Bézier finite elements on tetrahedral–hexahedral–pyramidal partitions Computer Methods in Applied Mechanics and Engineering. 2016; 304 : 140-170 . full text
- Zayernouri, Mohsen, Ainsworth, Mark, Karniadakis, George Em. A unified Petrov–Galerkin spectral method for fractional PDEs Computer Methods in Applied Mechanics and Engineering. 2015; 283 : 1545-1569 . full text
- Ainsworth, Mark, Barrenechea, Gabriel R., Wachtel, Andreas. Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow SIAM Journal on Numerical Analysis. 2015; 53 (2) : 1107-1120 . full text
- Ainsworth, Mark, Andriamaro, Gaelle, Davydov, Oleg. A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements Constr Approx. 2014; 41 (1) : 1-22 . full text
- Ainsworth, Mark. Dispersive behaviour of high order finite element schemes for the one-way wave equation Journal of Computational Physics. 2014; 259 : 1-10 . full text
- Ainsworth, Mark. Pyramid Algorithms for Bernstein--Bézier Finite Elements of High, Nonuniform Order in Any Dimension SIAM J. Sci. Comput.. 2014; 36 (2) : A543-A569 . full text
- Ainsworth, Mark, Vejchodský, Tomáš. Robust error bounds for finite element approximation of reaction–diffusion problems with non-constant reaction coefficient in arbitrary space dimension Computer Methods in Applied Mechanics and Engineering. 2014; 281 : 184-199 . full text
- Ainsworth, Mark, Allendes, Alejandro, Barrenechea, Gabriel R., Rankin, Richard. Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions International Journal for Numerical Methods in Fluids. 2013 : n/a-n/a . full text
- Ainsworth, Mark, Allendes, Alejandro, Barrenechea, Gabriel R., Rankin, Richard. On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations SIAM Journal on Numerical Analysis. 2013; 51 (3) : 1585-1609 . full text
- Ainsworth, Mark, Rankin, Richard. Guaranteed computable bounds on quantities of interest in finite element computations International Journal for Numerical Methods in Engineering. 2012; 89 (13) : 1605-1634 . full text
- Ainsworth, Mark, Ma, Xinhui. Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity Journal of Computational Physics. 2012; 231 (2) : 436-453 . full text
- Ainsworth, Mark, Andriamaro, Gaelle, Davydov, Oleg. Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures SIAM J. Sci. Comput.. 2011; 33 (6) : 3087-3109 . full text
- Ainsworth, M., Allendes, A., Barrenechea, G. R., Rankin, R. Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem IMA Journal of Numerical Analysis. 2011; 32 (2) : 417-447 . full text
- Ainsworth, Mark, Vejchodský, Tomáš. Fully computable robust a posteriori error bounds for singularly perturbed reaction–diffusion problems Numer. Math.. 2011; 119 (2) : 219-243 . full text
- Ainsworth, Mark, Rankin, Richard. Realistic computable error bounds for three dimensional finite element analyses in linear elasticity Computer Methods in Applied Mechanics and Engineering. 2011; 200 (21-22) : 1909-1926 . full text
- Ainsworth, Mark, Rankin, Richard. Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes Numer. Methods Partial Differential Eq.. 2011; 28 (3) : 1099-1104 . full text
- Ainsworth, Mark. A framework for obtaining guaranteed error bounds for finite element approximations Journal of Computational and Applied Mathematics. 2010; 234 (9) : 2618-2632 . full text
- Ainsworth, Mark, Rankin, Richard. Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes SIAM Journal on Numerical Analysis. 2010; 47 (6) : 4112-4141 . full text
- Ainsworth, Mark, Wajid, Hafiz Abdul. Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration SIAM Journal on Numerical Analysis. 2010; 48 (1) : 346-371 . full text
- Mihai, L. Angela, Ainsworth, Mark. A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures Computer Methods in Applied Mechanics and Engineering. 2009; 199 (1-4) : 48-60 . full text
- Ainsworth, Mark, Mihai, L. Angela. An adaptive multi-scale approach to the modelling of masonry structures International Journal for Numerical Methods in Engineering. 2009; 78 (10) : 1135-1163 . full text
- Mihai, L.A., Ainsworth, Mark. An adaptive multi-scale computational modelling of Clare College Bridge Computer Methods in Applied Mechanics and Engineering. 2009; 198 (21-26) : 1839-1847 . full text
- Ainsworth, M., Rankin, R. Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes IMA Journal of Numerical Analysis. 2009; 31 (1) : 254-280 . full text
- Ainsworth, Mark, Wajid, Hafiz Abdul. Dispersive and Dissipative Behavior of the Spectral Element Method SIAM Journal on Numerical Analysis. 2009; 47 (5) : 3910-3937 . full text
- Ainsworth, Mark, Demkowicz, Leszek. Explicit polynomial preserving trace liftings on a triangle Mathematische Nachrichten. 2009; 282 (5) : 640-658 . full text
- Ainsworth, Mark, Rankin, Richard. Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity International Journal for Numerical Methods in Engineering. 2009; 82 (9) : 1114-1157 . full text
- Ainsworth, Mark. A Posteriori Error Estimation for Lowest Order Raviart–Thomas Mixed Finite Elements SIAM J. Sci. Comput.. 2008; 30 (1) : 189-204 . full text
- Ainsworth, Mark, Rankin, Richard. Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements SIAM Journal on Numerical Analysis. 2008; 46 (6) : 3207-3232 . full text
- Ainsworth, Mark, Rankin, Richard. Robust a posteriori error estimation for the nonconforming Fortin--Soulie finite element approximation Mathematics of Computation. 2008; 77 (264) : 1917-1939 . full text
- Ainsworth, Mark. A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation SIAM Journal on Numerical Analysis. 2007; 45 (4) : 1777-1798 . full text
- Ainsworth, Mark, Demkowicz, Leszek, Kim, Chang-Wan. Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes Computer Methods in Applied Mechanics and Engineering. 2007; 196 (37-40) : 3493-3507 . full text
- Ainsworth, Mark, Mihai, L. Angela. Modeling and numerical analysis of masonry structures Numer. Methods Partial Differential Eq.. 2007; 23 (4) : 798-816 . full text
- Ainsworth, Mark, Mihai, L. Angela. A comparison of solvers for linear complementarity problems arising from large-scale masonry structures Appl Math. 2006; 51 (2) : 93-128 . full text
- Ainsworth, M., Monk, P., Muniz, W. Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation J Sci Comput. 2006; 27 (1-3) : 5-40 . full text
- Ainsworth, Mark, Carstensen, Carsten, Dörfler, Willy. Mini-Workshop: Convergence of Adaptive Algorithms Oberwolfach Rep.. 2005 : 2091-2138 . full text
- Dörfler, W., Ainsworth, M. Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow Mathematics of Computation. 2005; 74 (252) : 1599-1620 . full text
- Ainsworth, Mark. Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation SIAM Journal on Numerical Analysis. 2005; 42 (6) : 2320-2341 . full text
- Ainsworth, Mark. Discrete Dispersion Relation for hp -Version Finite Element Approximation at High Wave Number SIAM Journal on Numerical Analysis. 2004; 42 (2) : 553-575 . full text
- Ainsworth, Mark. Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods Journal of Computational Physics. 2004; 198 (1) : 106-130 . full text
- Ainsworth, M. Dispersive properties of high-order Nedelec/edge element approximation of the time-harmonic Maxwell equations Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2004; 362 (1816) : 471-491 . full text
- Ainsworth, Mark, McLean, Bill, Tran, Thanh. Diagonal scaling of stiffness matrices in the Galerkin boundary element method The ANZIAM Journal. 2000; 42 (01) : 141 . full text