By William Fitzgibbon, Yuri A. Kuznetsov, Pekka Neittaanmäki, Olivier Pironneau

This quantity comprises 13 articles on advances in utilized arithmetic and computing equipment for engineering difficulties. Six papers are on optimization equipment and algorithms with emphasis on issues of a number of standards; 4 articles are on numerical equipment for utilized difficulties modeled with nonlinear PDEs; contributions are on summary estimates for blunders research; ultimately one paper offers with infrequent occasions within the context of uncertainty quantification. purposes comprise aerospace, glaciology and nonlinear elasticity.

Herein is a variety of contributions from audio system at meetings on utilized arithmetic held in June 2012 on the college of Jyväskylä, Finland. the 1st convention, “Optimization and PDEs with commercial purposes” celebrated the 70th birthday of Professor Jacques Périaux of the college of Jyväskylä and Polytechnic collage of Catalonia (Barcelona Tech) and the second one convention, “Optimization and PDEs with purposes” celebrated the seventy-fifth birthday of Professor Roland Glowinski of the college of Houston.

This paintings may be of curiosity to researchers and practitioners in addition to complex scholars or engineers in computational and utilized arithmetic or mechanics.

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**Example text**

Froese BD, Oberman AM (2011) Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation. J Comput Phys 230(3):818–834 15. Gilbarg D, Trudinger NS (2001) Elliptic partial differential equations of second order. Springer, Berlin (Reprint of the 1998 edition) 16. Glowinski R (2003) Finite element methods for incompressible viscous flow. In: Ciarlet PG, Lions JL (eds) Handbook of numerical analysis, vol IX. North-Holland, Amsterdam, pp 3–1176 17. Glowinski R (2008) Numerical methods for nonlinear variational problems.

10962. 3 Problems on Domains with Curved Boundaries Mixed low order finite elements allow to consider easily domains with curved boundaries. In order to illustrate this fact and the flexibility of the method, we consider here the spherical domain S1 = {(x, y, z) ∇ R3 , x 2 + y 2 + z 2 < 1}. Let us consider the data for the (σ2 ) problem f (x, y, z) = 1 and g(x, y, z) = 0. The corresponding (σ2 ) problem admits the exact, smooth, convex solution 1 ψ(x, y, z) = − ≥ (1 − x 2 − y 2 − z 2 ). 43) This solution admits its minimum at the center of the spherical domain.

Comput Methods Appl Mech Eng 150(1–4):327–350 46. Stein E, Rüter M, Ohnimus S (2007) Error-controlled adaptive goal-oriented modeling and finite element approximations in elasticity. Comput Methods Appl Mech Eng 196(37–40):3598–3613 47. Verfürth R (1996) A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner, New York 48. Wahlbin LB (1995) Superconvergence in Galerkin finite element methods. Lecture notes in mathematics, vol 1605. Springer, Berlin 22 I.