[1]

L. Banz, B. P. Lamichhane and E. P. Stephan,
Higher order FEM for the obstacle problem of the *p*-Laplacian – A variational inequality approach,
preprint, (2017).

[2]

L. Banz and A. Schröder,
Biorthogonal basis functions in *hp*-adaptive FEM for elliptic obstacle problems,
Comput. Math. Appl. 70 (2015), no. 8, 1721–1742.
CrossrefWeb of ScienceGoogle Scholar

[3]

L. Banz and E. P. Stephan,
A posteriori error estimates of *hp*-adaptive IPDG-FEM for elliptic obstacle problems,
Appl. Numer. Math. 76 (2014), 76–92.
CrossrefWeb of ScienceGoogle Scholar

[4]

L. Banz and E. P. Stephan,
hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems,
Comput. Math. Appl. 67 (2014), 712–731.
Web of ScienceCrossrefGoogle Scholar

[5]

J. W. Barrett and W. Liu,
Quasi-norm error bounds for the finite element approximation of a non-Newtonian flow,
Numer. Math. 68 (1994), no. 4, 437–456.
CrossrefGoogle Scholar

[6]

S. Bartels and C. Carstensen,
Averaging techniques yield reliable a posteriori finite element error control for obstacle problems,
Numer. Math. 99 (2004), 225–249.
CrossrefGoogle Scholar

[7]

D. Braess,
A posteriori error estimators for obstacle problems–another look,
Numer. Math. 101 (2005), no. 3, 415–421.
CrossrefGoogle Scholar

[8]

D. Braess, C. Carstensen and R. Hoppe,
Convergence analysis of a conforming adaptive finite element method for an obstacle problem,
Numer. Math. 107 (2007), 455–471.
CrossrefWeb of ScienceGoogle Scholar

[9]

S. C. Brenner and L. R. Scott,
The Mathematical Theory of Finite Element Methods, 3 ed.,
Springer, New York, 2008.
Google Scholar

[10]

C. Carstensen and J. Hu,
An optimal adaptive finite element method for an obstacle problem,
Comput. Methods Appl. Math. 15 (2015), 259–277.
Web of ScienceGoogle Scholar

[11]

C. Carstensen and R. Klose,
A posteriori finite element error control for the *p*-Laplace problem,
SIAM J. Sci. Comput. 25 (2003), no. 3, 792–814.
CrossrefGoogle Scholar

[12]

C. Carstensen, W. Liu and N. Yan,
A posteriori FE error control for *p*-Laplacian by gradient recovery in quasi-norm,
Math. Comp. 75 (2006), no. 256, 1599–1616.
CrossrefGoogle Scholar

[13]

M. Chipot,
Elliptic Equations: An Introductory Course,
Birkhäuser, Basel, 2009.
Google Scholar

[14]

L. Diening and C. Kreuzer,
Linear convergence of an adaptive finite element method for the *p*-Laplacian equation,
SIAM J. Numer. Anal. 46 (2008), no. 2, 614–638.
Web of ScienceCrossrefGoogle Scholar

[15]

C. Ebmeyer and W. Liu,
Quasi-norm interpolation error estimates for the piecewise linear finite element approximation of *p*-Laplacian problems,
Numer. Math. 100 (2005), no. 2, 233–258.
CrossrefGoogle Scholar

[16]

J. Gwinner,
*hp*-FEM convergence for unilateral contact problems with Tresca friction in plane linear elastostatics,
J. Comput. Appl. Math. 254 (2013), 175–184.
Web of ScienceCrossrefGoogle Scholar

[17]

S. Hüeber and B. Wohlmuth,
A primal–dual active set strategy for non-linear multibody contact problems,
Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 27–29, 3147–3166.
CrossrefGoogle Scholar

[18]

G. Jouvet and E. Bueler,
Steady, shallow ice sheets as obstacle problems: Well-posedness and finite element approximation,
SIAM J. Appl. Math. 72 (2012), no. 4, 1292–1314.
Web of ScienceCrossrefGoogle Scholar

[19]

R. Krause, B. Müller and G. Starke,
An adaptive least-squares mixed finite element method for the signorini problem,
Numer. Methods Partial Differential Equations 33 (2017), 276–289.
CrossrefWeb of ScienceGoogle Scholar

[20]

A. Krebs and E. Stephan,
A *p*-version finite element method for nonlinear elliptic variational inequalities in 2D,
Numer. Math. 105 (2007), no. 3, 457–480.
Web of ScienceGoogle Scholar

[21]

B. Lamichhane and B. Wohlmuth,
Biorthogonal bases with local support and approximation properties,
Math. Comp. 76 (2007), no. 257, 233–249.
CrossrefGoogle Scholar

[22]

M. Lewicka and J. J. Manfredi,
The obstacle problem for the *p*-Laplacian via optimal stopping of tug-of-war games,
Probab. Theory Related Fields 167 (2017), no. 1–2, 349–378.
CrossrefWeb of ScienceGoogle Scholar

[23]

W. Liu and N. Yan,
Quasi-norm local error estimators for *p*-Laplacian,
SIAM J. Numer. Anal. 39 (2001), no. 1, 100–127.
CrossrefGoogle Scholar

[24]

W. Liu and N. Yan,
On quasi-norm interpolation error estimation and a posteriori error estimates for *p*-Laplacian,
SIAM J. Numer. Anal. 40 (2002), no. 5, 1870–1895.
CrossrefGoogle Scholar

[25]

M. Maischak and E. P. Stephan,
Adaptive *hp*-versions of BEM for Signorini problems,
Appl. Numer. Math. 54 (2005), no. 3, 425–449.
CrossrefGoogle Scholar

[26]

D. Malkus,
Eigenproblems associated with the discrete LBB condition for incompressible finite elements,
Internat. J. Engrg. Sci. 19 (1981), no. 10, 1299–1310.
CrossrefGoogle Scholar

[27]

J. M. Melenk,
*hp*-interpolation of nonsmooth functions and an application to *hp*-a posteriori error estimation,
SIAM J. Numer. Anal. 43 (2005), no. 1, 127–155.
CrossrefGoogle Scholar

[28]

N. Ovcharova and L. Banz,
Coupling regularization and adaptive *hp*-BEM for the solution of a delamination problem,
Numer. Math. 137 (2017), 303–337.
Web of ScienceCrossrefGoogle Scholar

[29]

J. Qin,
On the convergence of some low order mixed finite elements for incompressible fluids,
Ph.D. thesis, The Pennsylvania State University, 1994.
Google Scholar

[30]

A. Veeser,
Efficient and reliable a posteriori error estimators for elliptic obstacle problems,
SIAM J. Numer. Anal. 39 (2001), no. 1, 146–167.
CrossrefGoogle Scholar

[31]

T. Wick,
An error-oriented Newton/inexact augmented Lagrangian approach for fully monolithic phase-field fracture propagation,
SIAM J. Sci. Comput. 39 (2017), no. 4, B589–B617.
Web of ScienceGoogle Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.