NOVELTY - A high power density solid oxide fuel cell having a graded anode is produced by using a powder mixture of nickel oxide and yttria stabilized zirconia (YSZ). The YSZ contains 5-15 mol% of yttria doped zirconia. A reduced fuel cell is produced having thicker and thinner anodes. The thicker anode has an open porosity of 30-40 vol.%, and the thinner anode has a porosity of 20-29.9 vol.%.    USE - The method is used for producing a high power density solid oxide fuel cell.    ADVANTAGE - The method produces solid oxide fuel cell having superior power densities as well as improved durability and mechanical reliability. The graded porosity of the anode allows easy transport of fuel gases, thus minimizing concentration polarization.    DETAILED DESCRIPTION - Production of high power density solid oxide fuel cell having a graded anode involves obtaining a first powder mixture of nickel oxide (NiO) and yttria stabilized zirconia (YSZ). The YSZ contains 5-15 mol% of yttria (Y2O3) doped zirconia (ZrO2). The ratio of NiO to YSZ is 70-90 vol.% of the total volume of the mixture. A pellet of 100-3000 microns thick is created by consolidating the first powder mixture. Another powder mixture of NiO and YSZ is formed having 50-65 vol.% of NiO, and is added with water and alcohol to form a slurry. The pellet is contacted with the slurry, and the alcohol is evaporated to produce a graded pellet. A layer of YSZ is deposited on top surface of the graded pellet, and the pellet is sintered in air at 1100-1500 degreesC producing densification of the pellet in three layers. The three layers comprise YSZ electrolyte, NiO plus YSZ inner electrode layer, and NiO plus YSZ outer anode and support. The YSZ electrolyte has a porosity of less than 4 vol.%. A mixture of at least three components is calcined at 800-1200 degreesC to obtain a powdered mixture of lanthanum strontium magnesium (LSM). The three components comprise manganese oxide (MnO2); lanthanum oxide (La2O3), Y2O3 and any rare earth element oxide; and carbonates of strontium, calcium, barium, and/or magnesium. A powdered YSZ is also calcined at 1000-1300 degreesC. The powder mixtures of LSM and YSZ are mixed in the presence of organic liquid. The sintered pellet is then successively coated with the obtained powder mixtures of LSM and YSZ, and heated at 350-500 (preferably 400)degreesC in air or oxygen to produce a layer of 5-100 microns thick. The coated pellet is again heated at 1000-1400 (preferably 1250)degreesC to create unreduced fuel cell. The unreduced fuel cell is contacted with water and hydrogen at 500-1000 degreesC to produce reduced fuel cell having thicker and thinner anodes. The thicker anode has an open porosity of 30-40 vol.%, and the thinner anode has a porosity of 20-29.9 vol.%.    An INDEPENDENT CLAIM is also included for an improved anode fuel cell produced by the method. The fuel cell has a porosity graded anode of at least two different porosities. The anode layer adjacent to the electrolyte has a porosity of 10-30% and a thickness of 5-100 microns. The anode layer further to the electrolyte has a porosity of 20-50% and a thickness of 100-3000 microns.